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Question

If a2+b2=13 and ab=6 find 3(a+b)2−2(a−b)2.

A
14
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B
89
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C
45
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D
73
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Solution

The correct option is D 73
3(a+b)22(ab)2
We know,
(a+b)2=a2+b2+2ab
=13+2(6)
=13+12
=25
=>(a+b)=±25
=>(a+b)=±5
Again,
(ab)2=a2+b22ab
=132(6)
=1312
=1
=>(ab)=±1
Putting the values, we get,
3(±5)22(±1)2
=752
=73

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