ICSE Class X Math 2015 Solved Paper
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Question : 23
Total: 52
If a , b , c
( a + b + c ) ( a − b + c ) = a 2 + b 2 + c 2 .
Solution:
To Prove : ( a + b + c ) ( a − b + c ) = a 2 + b 2 + c 2
Proof :a , b , c
∴
=
= k (let)
b = c k
a = b k = ( c k ) k
= c k 2
L.H.S. = ( c k 2 + c k + c ) ( c k 2 − c k + c )
= c 2 ( k 2 + k + 1 ) ( k 2 − k + 1 )
= c 2 [ ( k 2 + 1 ) 2 − ( k ) 2 ]
= c 2 [ k 4 + 2 k 2 + 1 − k 2 ]
= c 2 [ k 4 + k 2 + 1 ]
R.H.S. = c 2 k 4 + c 2 k 2 + c 2
= c 2 [ k 4 + k 2 + 1 ]
L.H.S. = R.H.S.
Proof :
L.H.S. = R.H.S.
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