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# In the equation above, x =

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Math Expert
Joined: 02 Sep 2009
Posts: 52164
In the equation above, x =  [#permalink]

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29 Mar 2017, 01:42
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:07) correct 25% (01:06) wrong based on 167 sessions

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$$x(5+\sqrt{7})=90$$
In the equation above, x =

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

B. 15/2

C. 45

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

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

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

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29 Mar 2017, 02:20
4
1
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. $$90(5+\sqrt{7})$$

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

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

$$x = (90*(5-\sqrt{7}))/((5+\sqrt{7})*(5-\sqrt{7}))$$

$$x = (90*(5-\sqrt{7}))/(25-7)$$

$$x = (90*(5-\sqrt{7}))/18$$

$$x = 5*(5-\sqrt{7})$$

Hence option A is correct
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Re: In the equation above, x =  [#permalink]

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16 Oct 2018, 17:14
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)

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

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16 Oct 2018, 18:59
1
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]

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13 Jan 2019, 15:44
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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14 Jan 2019, 18:08
1
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 = &nbs [#permalink] 14 Jan 2019, 18:08
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