Question

plzzzz solve it also

Answer 1

hey friend!!!

(1)
Given x = 3 – 2√2

⇒ x = 2 + 1 – 2√2
⇒ x = (√2)2 + 12 – 2 × √2 × 1
⇒ x = (√2 – 1 )2
∴ √x = (√2 – 1 )
Now consider, (1/√x) = 1/(√2 – 1 )
Multiply and divide with (√2 + 1 ), we get
(1/√x) = (√2 + 1 )/[(√2 – 1 )(√2 + 1 )]
= (√2 + 1 )/[2 – 1]
∴ (1/√x) = (√2 + 1 )
√x + (1/√x) = (√2 – 1) + (√2 + 1) = "2√2"

(2)
x = 2 + ∫3 , 1/x = 2-∫3
So, x + 1/x = 4
(x+1/x)3 = 43
x3 + 1/x3 + 3x + 1/x = 64
x3 + 1/x3 + 3 = 64
x3 + 1/x3 = 64 – 3 = "61"


(3)
X=5-2√6
∴, x²=(5-2√6)²=25-2.5.2√6+24=49-20√6
1/x²=1/(5-2√6)²=1/(49-20√6)=(49+20√6)/(49-20√6)(49+20√6)=(49+20√6)/(2401-2400)=49+20√6
∴, x²+1/x²=49-20√6+49+20√6="98"

hope it will help you..