Question

if x square =11 +2 root 30, find x+1 by x​

Answer 1

Answer:

$\large{\underline{\boxed{\sf x + \frac{1}{x} = 2 \sqrt{6}}}}$

Step-by-step explanation:

Given that -

x² = 11 + 2√30

$\implies \tt \frac{1}{x {}^{2} } = \frac{1}{11 + 2 \sqrt{30} } \\ \\ \implies \tt \frac{1}{ {x}^{2} } = \frac{1}{11 + 2 \sqrt{30} } \times \frac{11 - 2 \sqrt{30} }{11 - 2 \sqrt{30} } \\ \\ \implies \tt \frac{1}{ {x}^{2} } = \frac{11 - 2 \sqrt{30} }{(11) {}^{2} - (2 \sqrt{30}) {}^{2}} \\ \\ \implies \tt \frac{1}{ {x}^{2} } = \frac{11 - 2 \sqrt{30} }{121 - 120} \\ \\ \implies \tt \frac{1}{x {}^{2} } = 11 - 2 \sqrt{30}$

Now,

$\implies \tt x {}^{2} + \frac{1}{ {x}^{2} } = 11 + 2 \sqrt{30} + 11 - 2 \sqrt{30} \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } = 11 + 11 \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } =22$

Adding 2 both the sides-

$\implies \tt {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 22 + 2 \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } + 2 \: . \: x \: .\: \frac{1}{x} = 24 \\ \\ \implies \tt ( x+ \frac{1}{x}) {}^{2} =24 \\ \\ \implies \tt x + \frac{1}{x} = \sqrt{24} \\ \\ \boxed{ \bf \therefore x + \frac{1}{x} = 2 \sqrt{6} }$

Answer 2

Answer:

(X+1)/X=(√6+√5+1)/( √5+√6)

Step-by-step explanation

X2=11+2√ 30

X=√ (11+√ 30)

X=√ ((√ 6)2+ (√ 5)2+ (2×√ 6×√ 5))

X=√6+√5

THEN (X+1)/X=(√6+√5+1)/( √5+√6)