1. Find two natural numbers whose sum is 50 and produet 525.

1.	1. Find two natural numbers whose sum is 50 and produet 525.
Answer» let the required no. be x and y so according to the question => x+ y = 50 -------(1) and => xy = 525 -------(2) so put y = 525/x in eqn (1) we get , => x + 525/x = 50 => x^2 + 525 = 50x => x^2 -50x +525 = 0 => x^2 -35x -15x + 525 =0 => x(x-35) -15(x-35) =0 => (x-35)(x-15) = 0 => x-35 = 0 or x-15 = 0 => x = 35 , 15 # so the required number is 35 and 15

Answer»

let the required no. be x and y

so according to the question

=> x+ y = 50 -------(1)

and => xy = 525 -------(2)

so put y = 525/x in eqn (1)

we get ,

=> x + 525/x = 50

=> x^2 + 525 = 50x

=> x^2 -50x +525 = 0

=> x^2 -35x -15x + 525 =0

=> x(x-35) -15(x-35) =0

=> (x-35)(x-15) = 0

=> x-35 = 0 or x-15 = 0

=> x = 35 , 15

# so the required number is 35 and 15

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