Maths-

General

Easy

Question

# Find the value of 𝑚 & 𝑛 to make a true statement.

(𝑚𝑥 + 𝑛𝑦)^{2} = 4𝑥^{2} + 12𝑥𝑦 + 9𝑦^{2}

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)

= m^{2}x^{2} + mnxy + mnxy + n^{2}y^{2}

= m^{2}x^{2} + 2mnxy + n^{2}y^{2}

Now, m^{2}x^{2} + 2mnxy + n^{2}y^{2} = 4𝑥^{2} + 12𝑥𝑦 + 9𝑦^{2}

Comparing both sides, we get

m^{2} = 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.

### Find the value of x. Identify the theorem used to find the answer.

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

### Find the gradient and y- Intercept of the line

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-

### x^{0} = ?

### x^{0} = ?

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

### Find the equation of a line that passes through and

Maths-General

Maths-

### The degree of 25x^{2}y^{23} is

### The degree of 25x^{2}y^{23} 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