**If the sum of two numbers is 11 and sum of their cubes is 737, find the sum of their squares.**

Answer :

Answer :

Let us consider x and y be two numbers

Then,

x + y = 11

x^{3} + y^{3} = 735 and x^{2} + y^{2} =?

Now,

x + y = 11

Let us cube on both the sides,

(x + y)^{3} = (11)^{3}

x^{3} + y^{3} + 3xy (x + y) = 1331

737 + 3x × 11 = 1331

33xy = 1331 – 737

= 594

xy = 594/33

xy = 8

We know that, x + y = 11

By squaring on both sides, we get

(x + y)^{2} = (11)^{2}

x^{2} + y^{2} + 2xy = 121 ^{2} x^{2} + y^{2} + 2 × 18 = 121

x^{2} + y^{2} + 36 = 121

x^{2} + y^{2} = 121 – 36

= 85

Hence sum of the squares = 85

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