Question

if x=2+,√2find the value of x squar +1/x squar​

Answer 1

Step-by-step explanation:

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Answer 2

given :-

x = 2 + √2

therefore x² = (2 + √2)²

using identity (a + b)² = a² + 2ab + b²

here, a = 2 and b = √2

= (2)² + 2(2)(√2) + (√2)²

= 4 + 4√2 + 2

= 6 + 4√2

therefore 1/x² = 1/(6 + 4√2)

rationalizing,

= 1/(6 + 4√2) × (6 - 4√2)/(6 - 4√2)

= (6 - 4√2)/[(6 + 4√2) (6 - 4√2)]

using identity (a + b) (a - b) = a² - b² in the denominator

= (6 - 4√2)/[(6)² - (4√2)²]

= (6 - 4√2)/(36 - 32)

= (6 - 4√2)/4

= [(2 × 3) - (2 × 2)√2]/(2 × 2)

= 3 - 2√2/2

hence, value of x² + 1/x²

= 6 + 4√2 + (3 - 2√2/2)

= 2(6 + 4√2)/2 + (3 - 2√2)/2

= (12 + 8√2)/2 + (4 - 2√2)/2

= (13 + 8√2 + 4 - 2√2)/2

= (17 + 6√2)/2 final ans