Question

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

Answer 1

Answer:

Option A and C

$x = + 3\sqrt{2}/2 \or x = - 3\sqrt{2}/2$

Step-by-step explanation:

Given equation

$4x^2 + 7 = 25\\=> 4x^2 = 25 - 7\\=>4x^2 = 18\\=> x^2 = 18/4\\=> x^2 = 9/2 \\=> \sqrt{x^2} =\sqrt{9/2} \\=> x = 3/\sqrt{2} \ or -3/\sqrt{2}$

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 $\sqrt{2}$

$x = + 3*\sqrt{2}/(\sqrt{2} *\sqrt{2}) \or x = -3*\sqrt{2}/(\sqrt{2} *\sqrt{2}) \\\\ x = + 3\sqrt{2}/2 \or x = - 3\sqrt{2}/2$

In the above equation we have rationalized the value of  $1/\sqrt{2}$

as in answer $\sqrt{2}$ is present in numerator and not in denominator.