Question

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Answer 1

a+b=12  ab=24
a)
a²+b²=(a+b)²-2ab= 12²-48=144-48=96
a³+b³=(a+b)(a²-ab+b²)=(a+b)(a²+b²-2ab)   { a²+b² am calculat mai sus: =96}
(a+b)(a²+b²-2ab) =12(96-48)=12·48=576
a⁴+b⁴=(a²+b²)²-2a²b²=96²-2(ab)²=96²-2·576=96²-1152=9216-1152=8064
a⁶+b⁶=(a³+b³)²-2a³b³=(a³+b³)²-2(ab)³=576²-2·24³=331776-27648 =304128
b)
1/a + 1/b = (b+a)/ab = (a+b)/ab=12/24=1/2
1/a² + 1/b² = (b²+a²)/a²b²=(a²+b²)/(ab)²=96/576=1/6
1/a³ + 1/b³ = (b³+a³)/a³b³=(a³+b³)/(ab)³=576/576·24=1/24
1/a⁴ + 1/b⁴ = (b⁴+a⁴)/a⁴b⁴=(a⁴+b⁴)/(ab)⁴=8064/576·576= 14/576= 7/288