Question

A³+b³=152, a+b=8,then ab=?

Answer 1

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Answer 2

Answer:

Answer:

a² + b² = 34

Step-by-step explanation:

a³+b³= 152 and ab = 15

We know that, (a+b)³= a³ + b³ + 3ab(a+b)

(a+b)³= 152 + 3×15(a+b)

Let (a+b) = x

So, x³= 152 + 45x

x³ - 45x = 152

x × (x²- 45) = 8 × 19

Let x = 8 and x²- 45 = 19

So, 8²- 45 = 19

64 - 45 = 19

19 = 19 (Approved)

So, a+b = x = 8

On squaring both sides

(a+b)² = 8²

a² + b² + 2ab = 64 ............(1)

Put ab = 15 in eq. (1)

a² + b² + 2×15 = 64

a² + b² + 30 = 64

a² + b² = 64 - 30

a² + b² = 34