Mathematics: Which statement describes how to solve 3sqrt(x^2-6)=3sqrt(2x+2) square both sides and then solves the resulting quadratic equations square both sides and then solve the resulting cubic equations cube both sides and then solve the resulting quadratic equations cube both sides and then solve the resulting cubic equations

Which statement describes how to solve 3sqrt(x^2-6)=3sqrt(2x+2)

alexbanda996

08.01.2022

Option 1 - Square both sides and then solves the resulting quadratic equations

Step-by-step explanation:

Given : Expression $3\sqrt{x^2-6}=3\sqrt{2x+2}$

To find : Which statement describes how to solve given expression?

Solution :

The best option to solve the given expression is 'Square both sides and then solves the resulting quadratic equations'.

Now, We apply the statement to prove it.

$3\sqrt{x^2-6}=3\sqrt{2x+2}$

Squaring both side,

$(3\sqrt{x^2-6})^2=(3\sqrt{2x+2})^2$

9(x^2-6)=9(2x+2)

9x^2-54=18x+18

9x^2-18x-72=0

x^2-2x-8=0 (Taking 9 common)

Solving the quadratic equation,

Applying middle term split,

x^2-2x+4x-8=0

x(x-2)+4(x-2)=0

(x-2)(x+4)=0

x=2,-4

Therefore, The solution of the expression is x=2,-4.

Hence, Option 1 is correct.

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