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705-805 Level|   Algebra|      
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Bunuel
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If p = (√8 + √7)/(√8 − √7) and q = (√8 − √7)/(√8 + √7), then the value 21 Feb 2020, 05:43
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If \(p = \frac{√8 + √7}{√8 − √7}\) and \(q = \frac{√8 − √7}{√8 + √7}\), then the value of \(p^2 + pq + q^2\) is


A. 899
B. 900
C. 901
D. 998
E. 999


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A
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If p = (√8 + √7)/(√8 − √7) and q = (√8 − √7)/(√8 + √7), then the value 21 Feb 2020, 06:02
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P^2+pa+q^2= (p+q)^2 -pq

pq=1
(P+q)^2 = (2*(√8^2+√7^2))^2 = 30^2

P^2+pa+q^2= (p+q)^2 -pq = 900 - 1= 899

My ans: A

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If p = (√8 + √7)/(√8 − √7) and q = (√8 − √7)/(√8 + √7), then the value 21 Feb 2020, 06:03
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\(p^2 + pq + q^2\)
\(=p^2 + 2pq + q^2 -pq\)
\(=(p+q)^2 -pq \).... equation (i)

Upon simplification we find,
Now, pq = 1.
and p+q = 30

Therefore, putting these value in equation (i),
\(=30^2 - 1\)
=900-1
=899 (ans)
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If p = (√8 + √7)/(√8 − √7) and q = (√8 − √7)/(√8 + √7), then the value 22 Feb 2020, 08:16
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Solution attached

Bunuel
If \(p = \frac{√8 + √7}{√8 − √7}\) and \(q = \frac{√8 − √7}{√8 + √7}\), then the value of \(p^2 + pq + q^2\) is


A. 899
B. 900
C. 901
D. 998
E. 999


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File comment: Solution
20200222_204515.jpg
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If p = (√8 + √7)/(√8 − √7) and q = (√8 − √7)/(√8 + √7), then the value 23 Feb 2020, 05:52
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Bunuel
If \(p = \frac{√8 + √7}{√8 − √7}\) and \(q = \frac{√8 − √7}{√8 + √7}\), then the value of \(p^2 + pq + q^2\) is


A. 899
B. 900
C. 901
D. 998
E. 999


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Show more

Given, \(p = \frac{√8 + √7}{√8 − √7}\)
--> \(p = \frac{(√8 + √7)(√8 + √7)}{(√8 − √7)(√8 + √7)} = \frac{(√8 + √7)^2}{(8 - 7)} = 8 + 7 + 2√56 = 15 + 2√56\)
& \(q = \frac{√8 − √7}{√8 + √7}\)
--> \(q = \frac{(√8 - √7)(√8 - √7)}{(√8 + √7)(√8 - √7)} = \frac{(√8 - √7)^2}{(8 - 7)} = 8 + 7 - 2√56 = 15 - 2√56\)

Also, \(pq = \frac{√8 + √7}{√8 − √7}*\frac{√8 - √7}{√8 + √7} = 1\)

\(p^2 + pq + q^2 = (p + q)^2 - pq = (15 + 2√56 + 15 - 2√56)^2 - 1 = (30)^2 - 1 = 900 - 1 = 899\)

Option A
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If p = (√8 + √7)/(√8 − √7) and q = (√8 − √7)/(√8 + √7), then the value 06 Jun 2024, 08:14
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Hello from the GMAT Club BumpBot!

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