Question

If a-b = 7 and a²+b² = 85 , then fine the value of a³-b³.

Answer 1

a-b=7 ⇒a=7+b .....(i)
a²+b²=85 ....(ii)

Sub eq 1 to eq 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
value of a
a-b=7
⇒if b=-9
a-(-9)=7
a =7-9
=-2
⇒if b=2
a-2=7
a = 7+2
=9

So the value of a³ - b³ either of them
(a,b) = (-2,-9)
a³-b³ = -2³ - (-9)³
= -8 +729
= 721
if (a,b) = (2,9)
a³-b³ = 2³ - 9³
= 8-729
= -721

Answer 2

given a-b=7
by squaring on both sides we have
a^2+b^2-2ab = 7^2 = 49
and given a^2+b^2 = 85
therefore 85-2ab = 49
ab=18
now let's go to the question
a^3-b^3 = (a-b)(a^2+b^2+ab)
a^3-b^3 = 7 x(85+18) = 7 x 103 = 721
hence 721 is the answer