Question

What is the solution to the equation?

4 x squared − 3 equals 77
Choose all answers that are correct.

A.
5 square root of 2

B.
2 square root of 5

C.
− 2 square root of 5

D.
− 5 square root of 2

Answer 1

The answers are B. 2 square root of 5 and C. − 2 square root of 5.

$4 x^{2} -3=77$
$4 x^{2} =77+3$
$4 x^{2} =80$
$x^{2} =80:4$
$x^{2} =20$
$x= \sqrt{20}$
$x= \sqrt{4*5}$
$x= \sqrt{4}* \sqrt{5}$

Since √4 could be either -2 or +2, the solutions are:
$x=2 \sqrt{5}$ or $x=-2 \sqrt{5}$