Find the sum of their squares.

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

Let us consider x and y be two numbers

Then,

x + y = 11

x³ + y³ = 735 and x² + y² =?

Now,

x + y = 11

Let us cube on both the sides,

(x + y)³ = (11)³

x³ + y³ + 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

x² + y² + 2xy = 121 ² x² + y² + 2 × 18 = 121

x² + y² + 36 = 121

x² + y² = 121 – 36

= 85

Hence sum of the squares = 85

More Solutions:

• Factories the following :
• Factorise 21py2 – 56py
• Factorise 2πr2 – 4πr
• Factorise 25abc2 – 15a2b2c
• Factorise 8×3 – 6×2 + 10x
• Factorise 18p2q2 – 24pq2 + 30p2q
• Factorise 15a (2p – 3q) – 10b (2p – 3q)
• Factorise 6(x + 2y)3 + 8(x +2y)2
• Factorise 10a(2p + q)3 – 15b (2p + q)2 + 35 (2p + q)
• Factorise x2 + xy – x – y
• Factorise 5xy + 7y – 5y2 – 7x