then find the value of (x2 +y2 )
2022
then find the value of (x2 +y2 )
- A.
14
- B.
12
- C.
13
- D.
16
Attempted by 10 students.
Show answer & explanation
Correct answer: A
Step 1: Rationalize x = (√3 + 1)/(√3 - 1) by multiplying numerator and denominator by (√3 + 1).
x = [(√3 + 1)(√3 + 1)] / [(√3 - 1)(√3 + 1)] = (3 + 2√3 + 1) / (3 - 1) = (4 + 2√3) / 2 = 2 + √3.
Step 2: Rationalize y = (√3 - 1)/(√3 + 1) by multiplying numerator and denominator by (√3 - 1).
y = [(√3 - 1)(√3 - 1)] / [(√3 + 1)(√3 - 1)] = (3 - 2√3 + 1) / (3 - 1) = (4 - 2√3) / 2 = 2 - √3.
Step 3: Compute x² + y².
x² = (2 + √3)² = 4 + 4√3 + 3 = 7 + 4√3.
y² = (2 - √3)² = 4 - 4√3 + 3 = 7 - 4√3.
x² + y² = (7 + 4√3) + (7 - 4√3) = 14.
हिन्दी उत्तर:
चरण 1: x = (√3 + 1)/(√3 - 1) को (√3 + 1) से अंश और हर को गुणा करके परिमेयीकृत करें।
x = [(√3 + 1)(√3 + 1)] / [(√3 - 1)(√3 + 1)] = (3 + 2√3 + 1) / (3 - 1) = (4 + 2√3) / 2 = 2 + √3.
चरण 2: y = (√3 - 1)/(√3 + 1) को (√3 - 1) से अंश और हर को गुणा करके परिमेयीकृत करें।
y = [(√3 - 1)(√3 - 1)] / [(√3 + 1)(√3 - 1)] = (3 - 2√3 + 1) / (3 - 1) = (4 - 2√3) / 2 = 2 - √3.
चरण 3: x² + y² की गणना करें।
x² = (2 + √3)² = 4 + 4√3 + 3 = 7 + 4√3.
y² = (2 - √3)² = 4 - 4√3 + 3 = 7 - 4√3.
x² + y² = (7 + 4√3) + (7 - 4√3) = 14.