Question
If x = (2+√3)/(2-√3), y = (2-√3)/(2+√3). Then
find out the value of (x²+y²-xy)/(x²+y²+xy)?Solution
x = (2+√3)/(2-√3) y = (2-√3)/(2+√3) So x+y = (2+√3)/(2-√3) + (2-√3)/(2+√3) = ((2+√3)²+ (2-√3)²)/((2)²- (√3)²) = 2(4+3)/(4-3) {As (a+b)² + (a-b)² = 2(a^2+b^2 )} = x+y = 14 = xy = 1 = (x^2+y^2-xy)/(x^2+y^2+xy) = ((x+y)²-3xy)/((x+y)²-xy) = ((14)^2- 3)/((14)^2-1) = (196-3)/(196 - 1) = 193/195
More Algebra Questions
- Find the value of the expression:
15 + 10 – 6 × [20 + 8 – 2 × (50 – 35)] (64 × 16) ÷ (4 × 16) 3 × 256 2 = 4 ?
[564 + 32 of 18 × 9 ÷ 12 + 162 ] ÷ 4 = ?
187 ÷ 5 ÷ 0.4 = ? – 24 × 2.4
- 40% of 225 – 25% of 120 = 15% of ?
181/8 + 51/4 – 63/8 = ? + 9/2
(3500 ÷ √1225) × √(20.25) = ? ÷ 4
(11/12) × (18/22) × (4/3) + 3 = ?2
What will come in the place of question mark (?) in the given expression?
(5/8) × 1600 + (2400 ÷ 25) = ?
- What will come in place of (?) in the given expression.
(14)² – (12)² = ?
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