Question

the difference of squares of two numbers is 180. the square of the smaller number is 8 times the larger number. find the two number.

Answer 1

let two nos. be x (larger) and y(smaller)  respectively

                     x2 - y2 =180
                     y2=8x

Answer 2

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Let us say, the speed of the train be x km/hr.

Time taken to cover 360 km = 360/x hr.

As per the question given,

⇒ (x + 5)(360-1/x) = 360

⇒ 360 – x + 1800-5/x = 360

⇒ x2 + 5x + 10x – 1800 = 0

⇒ x(x + 45) -40(x + 45) = 0

⇒ (x + 45)(x – 40) = 0

⇒ x = 40, -45

As we know, the value of speed cannot be negative.

Therefore, the speed of train is 40 km/h.