Algebric equation

Algebra Level 1

The sum of the squares of two corresponding numbers is 100. What are the numbers?

121 and 4442 36 and 64 33 and 66 6 and 8

Rudra Kanti Mitra by Rudra Kanti Mitra , 22, India

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3 solutions

Nihar Mahajan
Feb 4, 2015

Let the numbers be a , b a , b

a 2 + b 2 = 1 0 2 a^2 + b^2 = 10^2

We know that this equation has solution of Pythagorean triplet 6 , 8 , 10 6,8,10 which is unique.

Hence , ( a , b ) = ( 6 , 8 ) (a,b)=(6,8)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes, this is the only solution by the Pythagorean's theorem, but how can it be proved?

Luciano Canela - 6 years, 4 months ago

only the last one fitted..DEDUCTIVE REASONING!!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

LET THE FIRST NO BE -X THEN; X2+(X+2)2=100

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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