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

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Math Expert
Joined: 02 Sep 2009
Posts: 46167
If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink]

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12 Sep 2017, 05:22
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:33) correct 24% (01:17) wrong based on 74 sessions

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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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BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2820
Location: India
GPA: 3.12
If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink]

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12 Sep 2017, 05:28
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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Manager
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink]

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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
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: If a – b = 7 and 2ab = 18 then a^2 + b^2 = [#permalink]

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15 Sep 2017, 10:07
1
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

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Re: If a – b = 7 and 2ab = 18 then a^2 + b^2 =   [#permalink] 15 Sep 2017, 10:07
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