Question

x=√2+1/√2-1 and y= √2-1/√2+1 show that x²+ y²+xy =35​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

• x = (√2 + 1)/(√2 - 1)
• y = (√2 - 1)/(√2 + 1)

To Proof,

• x²+ y²+ xy =35

Proof,

By Rationalizing the denominator,

x = (√2 + 1)/(√2 - 1)

x = (√2 + 1)/(√2 - 1) × (√2 + 1)/(√2 + 1)

x = ((√2)² + 2√2 × 1 + 1²)/((√2)²- 1²)

x = (2 + 1 + 2√2)/1

x = 3 + 2√2

By Rationalizing the denominator,

y = (√2 - 1)/(√2 + 1)

y = (√2 - 1)/(√2 + 1) × (√2 - 1)/(√2 - 1)

y = ((√2)² - 2√2 × 1 + 1²)/((√2)² - 1²)

y = (2 - 2√2 + 1)/1

y = 3 - 2√2

x² + y² + xy = 35

x² + y² + 2xy - xy = 35

(x + y)² - xy = 35

(3 + 2√2 + 3 - 2√2)² - (3 + 2√2)(3 - 2√2) = 35

6² - (3² - (2√2)²) = 35

36 - (9 - 8) = 35

36 - 1 = 35

35 = 35

L.H.S. = R.H.S.

••••••••••••••• Hence Proved