1.

If a^3+b^3=152 and ab=15 then what is value of a^2+b^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


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