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!