Question

if x is equals to 7 + root 40 then find the value of root x plus one upon root x

Answer 1

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Answer 2

Answer:

(4√5+2√2)/3

Step-by-step explanation:

Given

x= 7+√40

To find = √x+1/√x

Now,

x= 7+√40

it can be written as

x = 7+2√10

or, x = 5+2+ 2√10

x = (√5)²+(√2)²+ 2√5*√2

Compare with (a+b)² = a²+b²+ 2 a b

a = √5 and b= √2

So

x= (√5+√2)²]

√x = √5+√2

√x+ 1/√x = √5+√2 + 1/√5+√2

Rationalise 1 /√5+√2 = √5-√2 / (√5+√2)*√5-√2

= (√5-√2)/(5-2)

= (√5-√2)/3

√x+ 1/√x = √5+√2+ √5-√2/3

= (3√5+3√2+√5-√2)/3

= (4√5+2√2)/3

Hence, √x+ 1/√x = (4√5+2√2)/3