ScottTargetTestPrep wrote:

Bunuel wrote:

\(x(5+\sqrt{7})=90\)

In the equation above, x =

A. \(5(5-\sqrt{7})\)

B. 15/2

C. 45

D. \(90(5-\sqrt{7})\)

E. \(90(5+\sqrt{7})\)

Simplifying we have:

x = 90/(5 + √7)

We must rationalize the denominator by multiplying numerator and denominator of the right side of the equation by the conjugate of (5 + √7). The conjugate of (5 + √7) is (5 - √7). Multiplying the rightside by (5 - √7)/(5 - √7), we have:

90(5 - √7)/(25 - 7) = 90(5 - √7)/18 = 5(5 - √7)

Answer: A

Hello ScottTargetTestPrep !

Why usually when we rationalize the denominator it ends up being 1 but in this case is not?

I have seen a lot of examples here that people automatically put a 1 after this kind of terms:

(5 + √7)(5 - √7) = 1 (Now I know is not 1)

Should we have to solve it in all cases?

Kind regards!