Maths-
General
Easy
Question
Find the value of 𝑚 & 𝑛 to make a true statement.
(𝑚𝑥 + 𝑛𝑦)2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2
Hint:
The methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2
The correct answer is: (2,2) and (-2,-2).
(mx + ny)2 can be written as (mx + ny)(mx + ny)
(mx + ny)(mx + ny) = mx(mx + ny) + ny(mx + ny)
= mx(mx) + mx(ny) + ny(mx) + ny(ny)
= m2x2 + mnxy + mnxy + n2y2
= m2x2 + 2mnxy + n2y2
Now, m2x2 + 2mnxy + n2y2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2
Comparing both sides, we get
m2 = 4, n = 9, 2mn = 12
So, m = +2 or -2 , n = +3 or -3
Considering 2mn = 12, there are two combinations possible
- m = +2 and n = +2
- m = -2 and n = -2
Final Answer:
Hence, the values of (m, n) are (2,2) and (-2,-2).
Related Questions to study
Maths-
37. In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
i)Which equation models the scoring in the final round and the outcome of the contest
A symbol (usually a letter) in algebra represents an unknown numerical value in an algebraic expression or an equation. A variable is a non-fixed quantity that can be changed. Variables are essential because they are a significant component of algebra.
¶ Different Types of Variables
¶Dependent Variables: The variables whose values are determined by another variable's quantity.
¶Unrelated Variables: The values of an independent variable in an algebraic equation are unaffected by changes. Suppose an algebraic equation has two variables, x and y, and each x value is related to any other y value. In that case, x is an independent variable, and y is a dependent variable.
37. In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
i)Which equation models the scoring in the final round and the outcome of the contest
Maths-General
A symbol (usually a letter) in algebra represents an unknown numerical value in an algebraic expression or an equation. A variable is a non-fixed quantity that can be changed. Variables are essential because they are a significant component of algebra.
¶ Different Types of Variables
¶Dependent Variables: The variables whose values are determined by another variable's quantity.
¶Unrelated Variables: The values of an independent variable in an algebraic equation are unaffected by changes. Suppose an algebraic equation has two variables, x and y, and each x value is related to any other y value. In that case, x is an independent variable, and y is a dependent variable.
Maths-
Find the value of x. Identify the theorem used to find the answer.
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)
Find the value of x. Identify the theorem used to find the answer.
![](data:image/png;base64,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)
Maths-General
Maths-
Where is the circumcentre located in any right triangle? Write a coordinate proof of this result.
Where is the circumcentre located in any right triangle? Write a coordinate proof of this result.
Maths-General
Maths-
Ayush is choosing between two health clubs. Health club 1: Membership R s 22 and
Monthly fee R s 24.50. Health club 2: Membership R s 47.00 , monthly fee R s 18.25
. After how many months will the total cost for each health club be the same ?
Ayush is choosing between two health clubs. Health club 1: Membership R s 22 and
Monthly fee R s 24.50. Health club 2: Membership R s 47.00 , monthly fee R s 18.25
. After how many months will the total cost for each health club be the same ?
Maths-General
Maths-
Find the gradient and y- Intercept of the line ![x plus 2 y equals 14](data:image/png;base64,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)
Find the gradient and y- Intercept of the line ![x plus 2 y equals 14](data:image/png;base64,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)
Maths-General
Maths-
We can express any constant in the variable form without changing its value as
We can express any constant in the variable form without changing its value as
Maths-General
Maths-
x0 = ?
x0 = ?
Maths-General
Maths-
State and prove the Perpendicular Bisector Theorem.
State and prove the Perpendicular Bisector Theorem.
Maths-General
Maths-
What is a monomial? Explain with an example.
What is a monomial? Explain with an example.
Maths-General
Maths-
Find the equation of a line that passes through
and ![left parenthesis 2 comma negative 14 right parenthesis](data:image/png;base64,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)
Find the equation of a line that passes through
and ![left parenthesis 2 comma negative 14 right parenthesis](data:image/png;base64,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)
Maths-General
Maths-
The degree of 25x2y23 is
The degree of 25x2y23 is
Maths-General
Maths-
Ritu earns R s 680 in commission and is paid R s 10.25 per hour. Karina earns R s
410 in commissions and is paid R s 12.50 per hour. What will you find if you solve
for x in the equation 10.25x + 680 = 12.5x + 480
Ritu earns R s 680 in commission and is paid R s 10.25 per hour. Karina earns R s
410 in commissions and is paid R s 12.50 per hour. What will you find if you solve
for x in the equation 10.25x + 680 = 12.5x + 480
Maths-General
Maths-
If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then the triangle is ____ isosceles.
If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then the triangle is ____ isosceles.
Maths-General
Maths-
Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B. On which of the following segments must P be located?
Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B. On which of the following segments must P be located?
Maths-General
Maths-
A constant has a degree__________.
A constant has a degree__________.
Maths-General