Question

Identify all of the solutions of 4x2 + 7 = 25.

A. 32√2

B. 2√

C. −32√2

D. 32

Answer 1

Option A and C

`x = + 3√(2)/2 \or x = - 3√(2)/2\\`

Explanation:

Given equation

`4x^2 + 7 = 25\\=> 4x^2 = 25 - 7\\=>4x^2 = 18\\=> x^2 = 18/4\\=> x^2 = 9/2 \\=> √(x^2) =√(9/2) \\=> x = 3/√(2) \ or -3/√(2)`

In the above problem after finding value for x^2 we have found the square root of 9 which is 3 and 2 which is
`√(2)`

`x = + 3*√(2)/(√(2) *√(2)) \or x = -3*√(2)/(√(2) *√(2)) \\\\ x = + 3√(2)/2 \or x = - 3√(2)/2\\`

In the above equation we have rationalized the value of
`1/√(2)`

as in answer
`√(2)` is present in numerator and not in denominator.