The difference of the squares of two numbers is 45.The square of the s

1.	The difference of the squares of two numbers is 45.The square of the smaller number is 4 times thelarger number .Determine the numbers.Ans: 6,9(a he ecual then show that a
Answer» Let the numbers are x and yThen,x^2 - y ^2 = 45.............(1)x^2 = 4y......(2) Put value of x^2 in eq(1) 4y - y^2 = 45y^2 - 4y + 45 = 0y^2 - 9y + 5y + 45 = 0y(y - 9) + 5(y - 9) = 0(y - 9)(y +5) = 0y = 9, - 5 Put value of y = 9 in eq(2)x^2 = 4*9x^2 = 36x = 6 The numbers 6 and 9

The difference of the squares of two numbers is 45.The square of the smaller number is 4 times thelarger number .Determine the numbers.Ans: 6,9(a he ecual then show that a

Answer»

Let the numbers are x and yThen,x^2 - y ^2 = 45.............(1)x^2 = 4y......(2)

Put value of x^2 in eq(1)

4y - y^2 = 45y^2 - 4y + 45 = 0y^2 - 9y + 5y + 45 = 0y(y - 9) + 5(y - 9) = 0(y - 9)(y +5) = 0y = 9, - 5

Put value of y = 9 in eq(2)x^2 = 4*9x^2 = 36x = 6

The numbers 6 and 9