If (a + b) = 1 and (1/a) – 2b = 5/a then find the value of a2 + b2.
As, a2 + b2 = (a + b)2 – 2ab ------------- (1) (1/a) – 2b = 5/a 1/a – 5/a = 2b - 4/a = 2b 2ab = - 4 Substitute the values of 2ab and a + b in (1) a2 + b2 = 1 - (-4) = 5
The quadratic equation (p + 1)x 2 - 8(p + 1)x + 8(p + 16) = 0 (where p ≠ -1) has equal roots. find the value of p.
I. y/16 = 4/y
II. x3= (2 ÷ 50) × (2500 ÷ 50) × 42× (192 ÷ 12)
If α, β are the roots of the equation x² – px + q = 0, then the value of α2+β2+2αβ is
...(i) 2x² – 9x + 10 = 0
(ii) 4y² – 12y + 9 = 0
I. 84x² - 167x - 55 = 0
II. 247y² + 210y + 27 = 0
I. x2 – 10x + 21 = 0
II. y2 + 11y + 28 = 0
I. x2 – 18x + 81 = 0
II. y2 – 3y - 28 = 0
I. 6y2- 17y + 12 = 0
II. 15x2- 38x + 24 = 0
I. 22x² - 97x + 105 = 0
II. 35y² - 61y + 24 = 0
I. 3x2 - 16x - 12 = 0
II. 2y2 + 11y + 9 = 0
