Question

ICSE Mathematics for Class 9
(b) If the sum of the squares of three numbers is equal to the square of their sum, prove that the
sum of the products of the three numbers taking two at a time is equal to zero.

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Answer 1

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Question :-

If the sum of the squares of three numbers is equal to the square of their sum, prove that the

sum of the products of the three numbers taking two at a time is equal to zero.

let 3 no.s be a , b , c

Given :-

$(a + b + c )^2 = a ^2 + b ^2 + c^2$----------(i)

To prove :-

If :-

$(a + b + c )^2 = a ^2 + b ^2 + c^2$

then ;

ab + bc + ca = 0

formulae used :-

$(a + b + c )^2 = a ^2 + b ^2 + c^2+2(ab + bc + ca)$

step by step explanation :-

let

$(a + b + c )^2 = a ^2 + b ^2 + c^2 = x$

x = x + 2(ab+bc+ca)

2(ab + bc + ca )= x - x

ab + bc + ca = 0/2

ab + bc + ca = 0

.............Hence proved

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