Find two consecutive natural numbers , the sum of whose squares is 145 .
Chap:- Quadratic equations
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• Let one positive integer be M
and
• Another positive integer be M + 1.
» The square of two positive integers is 145.
A.T.Q.
=> (M)² + (M + 1)² = 145
=> M² + M² + 1 + 2M = 145
=> 2M² + 2M + 1 - 145 = 0
=> 2M² + 2M - 144 = 0
Take 2 common
=> 2(M² + M - 72) = 0
=> M² + M - 72 = 0
Factorise it
=> M² + 9M - 8M - 72 = 0
=> M(M + 9) -8(M + 9) = 0
=> (M - 8) (M + 9) = 0
=> M = 8, M = - 9(neglected)
So,
=> M + 1 = 8 + 1 = 9
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Two conservative natural numbers are 8 and 9.
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