Q5 of 242 Page 9

If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

Let the integer be ‘a’.

Given, an integer is added to its square, the sum is 90

⇒ a + a² = 90

⇒ a² + 10a – 9a – 90 = 0

⇒ a(a + 10) – 9(a + 10) = 0

⇒ (a – 9)(a + 10) = 0

⇒ a = -10, 9

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm². Find the sides of the squares.

The sum of two numbers is 48 and their product is 432. Find the numbers.

Find the whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.

Find two consecutive natural numbers whose product is 20.