Question

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the difference of square of the two natural no is 84.the square of the larger no is 25 times the smaller no find the no......​

Answer 1

HELLO DEAR

LET THE NUMBERS BE X AND Y

X² + Y² = 84 ......(1)

X² = 25Y......(2)

BY PUTTING THE VALUE OF X² ON THE EQN (1)

25Y + Y² = 84

Y² + 25Y - 84 = 0

Y² - 3Y + 28Y - 84 = 0

Y(Y - 3) +28(Y - 3) = 0

(Y + 28)(Y - 3)

Y = -28 , 3

IF Y = 3

X² = 25(3)

X = √75

X = 5√3

HOPE IT HELPS YOU DEAR FRIEND

THANKS

Answer 2

Answer:

Let two natural nos be x and y

difference of squares ,

${x}^{2} - {y}^{2} = 84$

Square of larger no is 25 times the other,

${x}^{2} = 25y$

From both equation ,

$25y - {y}^{2} = 84 \\ {y}^{2} - 25y + 84 = 0\\ {y}^{2} - 21y - 4y + 84 = 0 \\ y(y - 21) - 4(y - 21) = 0 \\ (y - 21)(y - 4) = 0$

y = 21 or 4

When y = 21 ,

$x = \sqrt{25 \times 21}$

it's an irrational number , so 21 is not possible

when y = 4

$x = \sqrt{25 \times 4} = 10$

So the numbers are 10 and 4