Question

if x=2/3+root 7 then (x-3)^2

Answer 1

Answer:

$x = \frac{2}{3} + \sqrt{7 } \\ (x - 3) ^{2} = {x}^{2} + {3}^{2} - 2 \times 3 \times x \\ = ( \frac{2}{3} + \sqrt{7 }) ^{2} + 9 - 6( \frac{2}{3} + \sqrt{7 }) \\ = { (\frac{2}{3} )}^{2} + ( { \sqrt{7} })^{2} + 2 \times \frac{2}{3} \times \sqrt{7} + 9 - 4 - 6 \sqrt{7} \\ = \frac{4}{9} + 7 + \frac{4 \sqrt{7} }{3} + 5 - 6 \sqrt{7} \\ = \frac{4}{9} + 12 + \frac{4 \sqrt{7} }{3} - 6 \sqrt{7} \\ = \frac{4 + 108}{9} + \frac{4 \sqrt{7 } - 18 \sqrt{7} }{3} \\ = \frac{112}{9} - \frac{14 \sqrt{7} }{3} \\ = \frac{112 - 42 \sqrt{7} }{9}$

Answer 2

Answer:

7

Step-by-step explanation:

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

Thank you