Question

if x=8+3√7the find value of x²+1/x²​

Answer 1

Step-by-step explanation:

the above is the step by step explanation

Answer 2

Solution

Given :-

• x = (8 + 3√7)

Find :-

• Value of x² + 1/x²

Explanation

First calculate 1/x,

➡1/x = 1/(8+3√7)

Rationalize denominator

➡1/x = (8 - 3√7)/(8+3√7)(8-3√7)

➡1/x = (8 - 3√7)/(64 - 63)

➡1/x = (8-3√7)/1

➡1/x = (8 - 3√7)

Squaring Both side ,

➡1/x² = (8 - 3√7)²

➡1/x² = 8² + (3√7)² - 2×8×3√7

➡1/x² = 64 + 63 - 48√7

➡1/x² = 127 - 48√7

Now, Calculate ( x² + 1/x²)

➡( x² + 1/x²) = (127 - 48√7) + (127 - 48√7)

➡( x² + 1/x²) = (127 + 127) + (48√7 + 48√7)

➡( x² + 1/x²) = 254 + 96√7

Hence

• Value of ( x² + 1/x²) will be = (256 + 96√7)

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Some Important Formula

★ (a+b)² = a² + b² + 2ab

★ (a - b)² = a² + b² - 2ab

★ (a³ - b³) = (a - b)(a² + b² + ab)

★ (a³ + b³) = (a + b)(a² + b² - ab)

★ (a² - b²) = (a-b)(a+b)

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