Question

The difference of the squares of two numbers is 45 the square of the smallest number is 4 times the larger number determine the numbers.

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Answer 1

Let the two numbers be a and b

a 2 −b 2

=45....(1)

b

2

=4a...(2)

Putting (2) in (1)a

2

−4a=45

a

2

−4a−45=0

a

2

−9a+5a−45=0

a(a−9)+5(a−9)=0

(a−9)(a+5)=0

a=9ora=−5

If a=5, b=25−b

2

=45

25−45=b

2 b

2 =20(Neglecting this value)

IF a=9

b=±6

=3 b=±6

Numbers are 9,6 or 9,-6

soory for answering

Answer 2

ANSWER-:

Let the larger number be ‘X’, so the smaller number will be ‘Y’. ∴ X2 – Y2 = 45 –––––

(i) ∵4X = Y2 ––––––

(ii) On simplifying further, Putting the value of Y2 = 4X from equation ––––––

(ii) X2 – 4X = 45 X2 – 4X – 45 =

X = – 5 or 9

∴ X = 9

∴ Y=√(4 x 9) ∴ Y = 6 ∴

THANKS BHAI !