Question

If a=6-√35, find the value of a²+1/a²
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Answer 1

Given :-

• a = ( 6 - √35)

To Find :-

• (a² + 1/a²) = ?

Solution :-

→ a = 6 - √35 ---------- Equation (1)..

→ 1/a = 1/(6 - √35)

Rationalising the RHS part we get,

→ 1/a = 1/(6 - √35) * [ (6 + √35) / (6 - √35) ]

Now, using (a + b)(a - b) = a² - b² in Denominator, we get,

→ 1/a = (6 + √35) / [ (6)² - (√35)²]

→ 1/a = (6 + √35) / (36 - 35)

→ 1/a = (6 + √35) / 1

→ 1/a = (6 + √35) --------- Equation (2).

Adding Equation (1) & (2), we get,

→ (a + 1/a) = (6 - √35) + (6 + √35)

→ (a + 1/a) = 6 + 6

→ (a + 1/a) = 12

Squaring Both sides now, we get,

→ (a + 1/a)² = 12²

using (a + b)² = a² + b² + 2ab in LHS, we get,

→ a² + 1/a² + 2 * a * 1/a = 144

→ (a² + 1/a²) + 2 = 144

→ (a² + 1/a²) = 144 - 2

→ (a² + 1/a²) = 142 (Ans.)

Similar Question :-

https://brainly.in/question/17100497 .

Answer 2

Given

Value of a = 6 - √35

To find

Value of (a² + 1/a²)

Solution

Here, a = 6 - √35

⇒ 1/a = 1/(6 - √35)

⇒ 1/a = (6 + √35)/[(6 + √35)(6 - √35)]

[By multiplying (6 + √35) in both numerator & denominator]

⇒ 1/a = (6 + √35)/(6² - (√35)²)

⇒ 1/a = (6 + √35)(36 - 35)

⇒ 1/a = (6 + √35)/1

⇒ 1/a = 6 + √35

Now we have to find value of a² + 1/a²

⇒ a² + 1/a²= (a)² + (1/a)²

⇒(6 - √35)² + (6 + √35)²

⇒ (6² - 2 × 6√35 + 35) + (6² + 2 × 6√35 + 35)

⇒ 36 - 12√35 + 35 + 36 + 12√35 + 35

⇒ 72 + 70

⇒ 142

Therefore,

Required value of a² + 1/a² = 142 .