Question

If a+b=8 and ab = 6, find the value of a3 + b3​

Answer 1

${(a + b)}^{2} = {8}^{2} \\ {a}^{2} + {b}^{2} + 2ab = 64 \\ {a}^{2} + {b}^{2} = 64 - 2(6) \\ {a}^{2} + {b}^{2} = 64 - 12 \\ {a}^{2} + {b}^{2} = 52$

Now,

${a}^{3} + {b}^{3} = (a + b)({a}^{2} + {b}^{2} - ab) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (8)(52 - 6) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8(46) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 368$

$<marquee> MARK BRAINLIEST$

Answer 2

HEY MATE

a+b=8(cubing both sides)

a3+b3+3a2b+3ab2=512

a3+b3+3ab(a+b)=512

a3+b3+3*6*8=512

a3+b3+144=512

a3+b3=512-144

a3+b3=368 @ns

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