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If a – b = 7 and 2ab = 18 then a^2 + b^2 =

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Bunuel
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If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink] New post   12 Sep 2017, 05:22
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If a – b = 7 and 2ab = 18 then a^2 + b^2 =

A. 67
B. 49
C. 40
D. 31
E. 14
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A
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If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink] New post   12 Sep 2017, 05:28
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Bunuel wrote:
If a – b = 7 and 2ab = 18 then a^2 + b^2 =

A. 67
B. 49
C. 40
D. 31
E. 14


Formula used : \((a-b)^2 = a^2 + b^2 - 2ab\)

Therefore, \(a^2 + b^2 = (a-b)^2 +2ab\)
Substituting values,
\(a^2 + b^2 = (7)^2 +18 = 49 + 18 = 67\)(Option A)
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Re: If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink] New post   13 Sep 2017, 00:21
Bunuel wrote:
If a – b = 7 and 2ab = 18 then a^2 + b^2 =

A. 67
B. 49
C. 40
D. 31
E. 14

a^2+b^2= (a-b)^2+2ab= 7^2+18=49+18=67
Ans:A
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Re: If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink] New post   15 Sep 2017, 10:07
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Bunuel wrote:
If a – b = 7 and 2ab = 18 then a^2 + b^2 =

A. 67
B. 49
C. 40
D. 31
E. 14


We can square the first equation and we have:

(a – b)^2 = 7^2

a^2 - 2ab + b^2 = 49

Substituting 18 for 2ab, we have:

a^2 - 18 + b^2 = 49

a^2 + b^2 = 67

Answer: A
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Re: If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink] New post   31 Jan 2021, 07:12
Bunuel wrote:
If a – b = 7 and 2ab = 18 then a^2 + b^2 =

A. 67
B. 49
C. 40
D. 31
E. 14


The key here is to recall the formula of \((a - b)^2\) as soon as you look at equations such as \(a - b = 7\) and \(2ab = 18\).

1. Now, \((a - b)^2 = a^2 + b^2 - 2ab\)
2. Substituting \(a - b = 7\) and \(2ab = 18\) we get, \(49 = a^2 + b^2 - 18\)
3. Solving the above equation, we get \(a^2 + b^2 = 67\)

Ans. A
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Re: If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink]
31 Jan 2021, 07:12
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