Find the value of α2 + β2 if α + β = 2 and the distance between points (1, α) and (β, 1)is 3 units
- 14
- 3
- 5
-
11
The correct answer is: D
Explanation
\(PQ = \sqrt{(β - 1)^{2} + (1 - α)^{2}}\\3 =\sqrt{(β^{2} -2β^{2} + 1 + 1 - 2α + α^{2})}\\
3 = \sqrt{(α^{2} + β^{2} - 2α + 2β + 2)}\\
3 = \sqrt{(α^{2} + β^{2} - 2(α + β) + 2)}\\
3 = \sqrt{(α^{2} + β^{2} - 2 * 2 + 2)}\\
3 = \sqrt{(α^{2} + β^{2} - 2)}\\
9 = (α^{2} + β^{2} - 2)\\
α^{2} + β^{2} = 9 + 2\\
α^{2} + β^{2} = 11\)