Question

If a-b=5,a²+b²=49
Find the value of a b

Answer 1

a-b = 7

a2+b2 = 85

a3+b3 = (a+b)(a2-ab+b2)

Now,

(a-b)2 = a2+b2-2ab

49 = 85-2ab

2ab = 36

ab = 18

Now We Need To Find The Value Of a+b

(a+b)2 = a2+b2+2ab

(a+b)2 = 85+2*18 = 85+36 = 121

a+b = 11

Now Substitute It In the identity

a3+b3 = (11)(85-18)

a3+b3 = 67*11 = 737

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Answer 2

Given

a^2+b^2=49...... (1)

a-b=5

Squaring both sides

(a-b)^2=(5)^2

a^2+b^2-2ab=25

49-2ab=25........(from1)

-2ab=25-49

-2ab=-24

ab=-24/-2

ab=12