14. If a - b = 7 and a3 – b3 = 133, find (i) ab (it) a2 + b2.
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Step-by-step explanation:
a-b=7
we know that a^3-b^3= (a-b) (a^2+b^2+ab)
133=7×(a^2+b^2+ab)
133/7=a^2+b^2+ab
19=a^2+b^2+ab
we know that a-b=7
a=b+7
19=(b+7) ^2+b^2+(b+7) b
19=b^2+49+14b+b^2+b^2+7b
19= 3b^2+21b+49
3b^2+21b+30=0
b^2+7b+10=0
b^2+5b+2b+10=0
b(b+5) +2(b+5) =0
(b+2) (b+5) =0
b=(-2, -5)
a=b+7
a=(5, 2)
[ab= -10]
a^2+b^2= (a+b)^2-2ab
(3)^2-2(-10)
9+20
[a^2+b^2=29]
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