Maths · Relations between roots and coefficients, nature of roots
If and find: the value of
If \( x-y=7 \) and \( x^{3}-y^{3}=133 ; \) find: the value of \( x y \)
- A. 12
- B. - -
- C. -10 \)
- D. 5
Step-by-step solution
Given x - y = 7 and x^3 - y^3 = 133. Using identity x^3 - y^3 = (x - y)(x^2 + xy + y^2), we get 133 = 7(x^2 + xy + y^2) => x^2 + xy + y^2 = 19. Also, (x - y)^2 = x^2 - 2xy + y^2 = 49. Subtracting the second from the first gives 3xy = -30 => xy = -10.