If the difference of the squares of two numbers is 45, the square of the smaller number is 4 times the larger number, then the numbers are

9, 6 o r 9, - 6

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5, 6 o r 5, - 6

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9, 5 o r 9, - 5

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none of these

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Solution

The correct option is A $9, 6 o r 9, - 6$
$W e t a k e t h e b i g g e r n u m b e r a s x & t h e s m a l l e r o n e a s y . T h e n, b y t h e f i r s t c o n d i t i o n, x^{2} - y^{2} = 45.......... (i) a n d y^{2} = 4 x . . . . . . . . (i i) S u b s t i t u t i n g y^{2} = 4 x i n (i i) w e g e t x^{2} - 4 x - 45 = 0 ⟹ (x + 5) (x - 9) = 0 ⟹ x = - 5, 9. W e r e j e c t x = - 5 b e c a u s e s u b s t i t u t i n g t h i s v a l u e o f x i n (i i) w e h a v e y^{2} = 4 \times (- 5) = - 20 i . e y i s n o t a r e a l n u m b e r . ∴ w e a c c e p t x = 9. S u b s t i t u t i n g t h i s v a l u e o f x i n (i i) w e h a v e y^{2} = 4 \times 9 ⟹ y = \pm 6. ∴ (x, y) = (9, 6) o r (9, - 6) . A n s - O p t i o n A .$

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Similar questions

The difference between squares of two numbers is 45, the square of smaller number is 4 times the larger number. Find the numbers

The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

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