Q18 of 39 Page 91

Solve for x: ; x ≠ 0, –1, 2.

Given,

⇒ 35x² – 25x = 23(2x² – 2x – 4)

⇒ 35x² – 25x = 46x² – 46x – 92

⇒ 11x² – 21x – 92 = 0

⇒ 11x² – 44x – 23x – 92 = 0

⇒ 11x(x – 4) – 23(x – 4) = 0

⇒ (11x – 23)(x – 4) = 0

⇒ x = 23/11 or x = 4

The sum of any two natural numbers is 8. Find the numbers if the sum of their reciprocals is 8/15.

Solve the following for x :

Find the two consecutive numbers whose squares have the sum 85. Find the two number using the quadratic formula.

If α and β are zeros of quadratic polynomial x² – 5x + 6 then find the value of α² + β².