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# If the sum of a and b is 6 and the product of a and b is 7, what is

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Math Expert
Joined: 02 Sep 2009
Posts: 46291
If the sum of a and b is 6 and the product of a and b is 7, what is [#permalink]

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19 Sep 2017, 01:51
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Difficulty:

25% (medium)

Question Stats:

88% (00:36) correct 12% (02:35) wrong based on 43 sessions

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If the sum of a and b is 6 and the product of a and b is 7, what is the value of a2 + b2?

A. 22
B. 24
C. 29
D. 36
E. 42

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Re: If the sum of a and b is 6 and the product of a and b is 7, what is [#permalink]

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19 Sep 2017, 02:07
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1
Bunuel wrote:
If the sum of a and b is 6 and the product of a and b is 7, what is the value of a2 + b2?

A. 22
B. 24
C. 29
D. 36
E. 42

Question, what is the value of $$a^2 + b^2$$?

We can combine all of the information we have :
- $$(a+b)^2$$ = $$a^2+2ab+b^2$$
- $$(6)^2 = a^2+b^2+2(7)$$
- $$36-14=a^2+b^2$$
- So, $$a^2+b^2=22$$.

A.
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Re: If the sum of a and b is 6 and the product of a and b is 7, what is [#permalink]

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19 Sep 2017, 02:13
Bunuel wrote:
If the sum of a and b is 6 and the product of a and b is 7, what is the value of a2 + b2?

A. 22
B. 24
C. 29
D. 36
E. 42

a+b = 6
ab = 7
a^2 + b^2 = (a+b)^2 - 2ab = (6)^2 - 2*7 = 36 - 14 = 22

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Re: If the sum of a and b is 6 and the product of a and b is 7, what is   [#permalink] 19 Sep 2017, 02:13
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