Question

If x=2/3+root7 then (x-3)^2=

Answer 1

Given :-

x = 2/(3 + √7)

By rationalizing, we get

= 2/(3 + √7) × (3 - √7)/(3 - √7)

= 2(3 - √7)/(3 + √7)(3 - √7)

= (6 - 2√7)/[(3)² - (√7)²]

= (6 - 2√7)/(9 - 7)

= (6 + 2√7)/2

= 2(3 + 1√7)/2

= 3 + √7

Therefore value of (x - 3)² :-

= [(3 + √7)² - 2(3 + √7)(3) + (3)²]

= [(3² + 6√7 + √7²) - 2(9 + 3√7) + 9]

= 9 + 6√7 + 7 - 18 - 6√7 + 3

= 9 + 7 - 18 + 9

= 18 - 18 + 7

= 7 Final answer!

Identity used :-

• (a - b)(a + b) = a² - b²

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

Answer 2

Answer:

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