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Question
If a − b = −8 and ab = −12, then a3 − b3 =
Options
−244
−240
−224
−260
Solution
To find the value of a3 − b3
Given `a-b = -8,ab =-12`
Using identity `(a-b)^3 = a^3 - b^3 -3ab(a-b)`
Here `a-b = -8,ab =-12`we get
`(-8)^3 = a^3 -b^3 -3ab(a-b)`
`(-8)^3 =a^3 -b^3 -3 xx -12 xx -8`
`-512 = a^3 -b^3 - 288`
Transposing -288 to left hand side we get
`- 512 + 288 = a^3 - b^3`
`-224 = a^3 - b^3`
Hence the value of `a^3 -b^3 `is -224 .
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