if a-b=7 & a^2+b^2=85 then find a^3-b^3
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a-b=7=>a=7+b.....(i)
a²+b²=85.....(ii)
substitution of equation 1 to equation 2.
(7+b)²+b²=85
49+14b+b²+b²=85
2b²+14b-36=0
b²+7b-18=0
(b+9)(b-2)=0
b=-9 v b=2
Find the value of a
a-b=7
=>if b=-9
a-(-9)=7
a=7-9
a=-2
=>if b=2
a=7+2
a=9
so value of a³-b³ there are 2 options
=>if (a,b) = (-2,-9)
a³-b³=-2³-(-9)³
= -8+729
= 721
=>if (a,b) = (2,9)
= a³-b³ = 2³-9³
= 8-729
= -721
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