2. the sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares.

IF THE SUM OF TWO NUMBERS IS 7 AND THE SUM OF THEIR CUBES IS 133 FIND THE SUM OF THEIR SQUARES? ============= They're small numbers, to trial and error is the easiest way. 1 & 6 --> 1 + 216 = 217 NG 2 & 5 --> 8 + 125 = 133 You can find the squares of 2 & 5. =============== If the numbers were larger, or not integers: x + y = 7 x^3 + y^3 = 133 Sub for y, y = 7-x ----- x^3 + (7-x)^3 = 133

The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.

Let a, b be the two numbers.
.'. a + b = 7 and a3 + b3 = 133
(a + b)3 = a3 + b3 + 3ab (a + b)

⇒ (7)3 = 133 + 3ab (7)⇒ 343 = 133 + 21ab⇒  21ab = 343 - 133 = 210⇒ 21ab = 210

⇒ ab= 10

Now a2 + b2 = (a + b)2 - 2ab
                     = 72 - 2 x 10 = 49 - 20 = 29

Concept: Expansion of Formula

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