62
If a3 - b3 = 56 and a - b = 2 then what is the value of a2 + b2?
- A12
- B20
- C28
- D32
Answer not set
Discussion 1
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CCommunity
a3 – b3 = (a – b)(a2 + ab + b2)
56 = 2(a2 + ab + b2)
28 = (a2 + ab + b2) ----(1)
Now, (a – b)2 = a2 – 2ab + b2 = 4 ----(2)
Solving equation (1) and (2),
a2 + ab + b2 = 28
a2 – 2ab + b2 = 4
3ab = 24
ab = 8
Therefore, a2 + 8 + b2 = 28 in (1)
And a2 + b2 = 28 – 8 = 20
56 = 2(a2 + ab + b2)
28 = (a2 + ab + b2) ----(1)
Now, (a – b)2 = a2 – 2ab + b2 = 4 ----(2)
Solving equation (1) and (2),
a2 + ab + b2 = 28
a2 – 2ab + b2 = 4
3ab = 24
ab = 8
Therefore, a2 + 8 + b2 = 28 in (1)
And a2 + b2 = 28 – 8 = 20