Maths-

General

Easy

Question

Solve the equation $square root of x plus 2 end root plus square root of 3 x plus 4 end root equals 2$

hint Hint:

Rearrange the equation and then solve for x.

The correct answer is: x = 7 or -1

Complete step by step solution:
Here we have the equation $square root of x plus 2 end root plus square root of 3 x plus 4 end root equals 2$
$not stretchy rightwards double arrow square root of x plus 2 end root equals 2 minus square root of 3 x plus 4 end root$
On squaring both the sides, we have $x plus 2 equals left parenthesis 2 minus square root of 3 x plus 4 end root right parenthesis left parenthesis 2 minus square root of 3 x plus 4 end root right parenthesis$
$not stretchy rightwards double arrow x plus 2 equals 4 minus 4 square root of 3 x plus 4 end root plus 3 x plus 4$
On subtracting, 3x and 8 from both the sides, we get
$not stretchy rightwards double arrow negative 2 x minus 6 equals negative 4 square root of 3 x plus 4 end root$
On squaring both the sides, we get
$table attributes columnspacing 1em end attributes row cell left parenthesis negative 2 x minus 6 right parenthesis squared equals 16 left parenthesis 3 x plus 4 right parenthesis end cell row cell not stretchy rightwards double arrow 4 x squared plus 24 x plus 36 equals 48 x plus 64 end cell row cell not stretchy rightwards double arrow 4 x squared minus 24 x minus 28 equals 0 end cell end table$
Now, this is a quadratic equation with a = 4, b = -24, c = -28
Roots can be found with, $x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
$x equals fraction numerator 24 plus-or-minus square root of 576 minus 4 cross times 1 cross times negative 28 end root over denominator 2 cross times 4 end fraction$
On solving, we get x = 7 or -1

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Solve the equation

Rearrange the equation and then solve for x.

The correct answer is: x = 7 or -1

Complete step by step solution:Here we have the equation On squaring both the sides, we have On subtracting, 3x and 8 from both the sides, we getOn squaring both the sides, we get Now, this is a quadratic equation with a = 4, b = -24, c = -28Roots can be found with, On solving, we get x = 7 or -1

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