Math, asked by zara972189, 1 year ago

Find two consecutive natural numbers , the sum of whose squares is 145 .

Chap:- Quadratic equations​

Answers

Answered by studentofclass12
9

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Answered by Anonymous
9

• 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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