Question

the sum of two no. is 25 and sum of their square is 425 then what will be their product

Answer 1

Let the numbers be a and b

a + b = 25

==> a = 25 - b..............(1)

a² + b² = 425

==> ( 25 - b )² + b² = 425 [ From (1) ]

==> 625 + b² - 50 b + b² = 425

==> 2 b² - 50 b + 200 = 0

==>   b² - 25 b + 100 = 0

==> b² - 20 b - 5 b + 100 = 0

==> b ( b - 20 ) - 5 ( b - 20 ) = 0

==> ( b - 20 )( b - 5 ) = 0

Either :

b - 20 = 0

b = 20

or :

b - 5 = 0

b = 5

When b = 20

a = 25 - 20

=5

When b = 5

a = 25-5

=20

The 2 numbers are 20 and 5

The product = 20×5

==> 100

The answer is 100

Hope it helps :)

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Answer 2

let the two nos. be x and y (x>y)

ACC to 1st condition,

x + y = 25. ......(1)

ACC to 2nd condition,

x² + y² = 425. ......(2)

from (1),

x = 25 - y ....(3)

put (3) in (2),

(25 - y)² + y² = 425

25² - 50y + y² + y² = 425

2y² - 50y + 625 - 425 = 0

2y² - 50y + 200 = 0

y² - 25y + 100 = 0

y² - 20y - 5y + 100 = 0

y(y-20) - 5(y-20) = 0

(y-5) (y-20) = 0

y = 5,20

y = 5. (coz y<x)

put y = 5 in (3)

x = 25 - 5

x = 20

now, product of x and y = 20*5 = 100