Question

If x= 5-2 √6 Then find the value of x² + 1/x²​

Answer 1

ANSWER :–

▪︎ x² + 1/x² = 98

EXPLANATION :–

GIVEN :–

▪︎ Value of x is 5 - 2√6

TO FIND :–

Value of x² + 1/x² = ?

SOLUTION :–

▪︎ We know that –

⇨ (a + b)² = a² + b² + 2ab

▪︎ Now put a = x and b = 1/x –

⇨ (x + 1/x)² = x² + 1/x² + 2(x)(1/x)

⇨ (x + 1/x)² = x² + 1/x² + 2

⇨ x² + 1/x² = (x + 1/x)² - 2 —————eq.(1)

▪︎ Now let's find (1/x) –

⇒ 1/x = 1/(5 - 2√6)

⇒ 1/x = [1/(5 - 2√6)][(5 + 2√6)/(5 + 2√6)]

⇒ 1/x = (5 + 2√6)/(25 - 24)

⇒ 1/x = 5 + 2√6

▪︎ Now put the value of x and 1/x in eq.(1) –

⇒ x² + 1/x² = (5 - 2√6 + 5 + 2√6)² - 2

⇒ x² + 1/x² = (10)² - 2

⇒ x² + 1/x² = 100 - 2

⇒ x² + 1/x² = 98

Answer 2

Answer:

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