If a - b = 4 and a3 - b3 = 88, then find the value of a2 - b2.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 8√(6).
| Understanding | Application |
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(a3 - b3)=( a - b)( a2 - b2 + ab) (a3 - b3)=(a - b){ (a - b)2 + ab} Given, a - b = 4 and a3 - b3 = 88. (a2 + b2)2(a2 - b2)2 = 4a2b2 |
(a3 - b3)=(a - b){ (a - b)2 + ab} 88 = 4 x {(4)2 + 3ab} 22= 16 +3ab 3ab = 22 - 16 = 6 ab = 2 (a - b)2 = a2 + b2 -2ab 42 = a2 + b2 -2 x 2 a2 + b2=16 + 4 = 20
(a2 + b2)2 - (a2 - b2)2 = 4a2b2 (20)2 - (a2 - b2)2 = 4 x 22 (a2 - b2)2 = 400 - 16 = 384 (a2 - b2)= (a2 - b2) = |