Question

if a-b = 3, a³-b³ = 63 find a²+b²

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Answer 1

Answer:

17

Step-by-step explanation:

a-b = 3

so,

(a-b)² = 9

a²+b²-2ab = 9 -------- (i)

a³-b³ = 63

(a-b)(a²+b²+ab) = 63

as (a-b) = 3

so,

3(a²+b²+ab) = 63

a²+b²+ab = 63/3

a²+b²+ab = 21

2(a²+b²+ab) = 2×21. ( multiplying both sides by 2)

2a² +2b²+2ab = 42 -------- (ii)

after adding (i) and (ii) we get

a²+b²-2ab + 2a²+2b²+2ab = 42+9

3a²+3b² = 51

3(a²+b²) = 51

a²+b² = 51/3

a²+b² = 17

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Answer 2

Identity : (a-b)^3 = a^3 - b^3 -3ab( a-b)

(3)^3 = 63 - 3ab(3)

27 -63 = -9ab
36/9 = ab
ab = 4

(a-b)^2 = a^2 + b ^2 + 2ab
(3)^2 = a^2 + b^2 + 2(4)
9-8= a^2 + b^2
1 = a^2 + b^2