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# In the equation above, x =

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Re: In the equation above, x = [#permalink]
1
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The best approach for solving this question is to simply put the answer choices one by one in place of x
By inputing answer choices in value of x, we get Option B as the answer where L.H.S=R.H.S.
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Re: In the equation above, x = [#permalink]
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)

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!
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Re: In the equation above, x = [#permalink]
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Hi jfranciscocuencag,

It sometimes ends up as 1; for example, (4 + √15) x (4 - √15) = 16 - 15 = 1; however in other examples the outcome is not 1.

For example, (4 + √14) x (4 - √14) = 16 - 14 = 2. More often, it is the latter case rather than the former, so never expect for the result to be 1 until you carry out the multiplication.
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Re: In the equation above, x = [#permalink]
I had considered that x must be between 90/(5+√9) & 90/(5+√4) [Since working with perfect squares is a lot easier].

Which roughly means 11<x<12

So A is the only option that is even remotely close to this range.

*Is this approach correct?*
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Re: In the equation above, x = [#permalink]

Solution

Given
• x(5+√7)=90

To find
• Value of x

Approach and Working out
• x(5+√7)=90
• x = 90 / (5+√7)
• Multiplying by (5-√7) in both numerator and denominator, we get:
o x =90(5-√7)/ (25-7)
o x =90(5-√7)/ 18
o x =5(5-√7)

Hence, option A is the correct answer.

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Re: In the equation above, x = [#permalink]
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Re: In the equation above, x = [#permalink]
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