Question

(√?-1)²=8-√28 Find Underoot​

Answer 1

Answer:

let x be the number under root

then (√x - 1)^2 = 8 - √28

=> x + 1 - 2√x = 8 - √28

=> x - 2√x = 8 - √28 - 1

=> x - 2√x = 7 - √28

=> x - 2√x = 7 - 2√7 [ √28 = √ 4×√7 = 2√7 ]

=> on comparing LHS and RHS,

we get x = 7

therefore under root is 7 Answer

Answer 2

Answer:

The value of x is 7

Step-by-step explanation:

Given:

(√x-1)² = 8- √28

To find the value of x

Solution:

Let, left hand side = L.H.S.

Let, right hand side = R.H.S.

Consider the L.H.S.,  

We know that, (a²- b²= a² + b² - 2ab)

Now, by applying the above formula,  

=>(√x)² + (1) - 2x (1) × (√x)

=>x+1 - 2× √x = 8 - √28

Consider the R.H.S.,

=>  8-√28 = 8 - (√7×4)

=> 8-√28 = 8 - (√7 ×(2)²)

Since,√2)² = 2, we get

=>8 -√28 = 8-2× (√7)

Hence, x+1 - 2 × √x = 8-2 × √(7)

=> x-2 × √x = 7 -2 × √(7)

=>√x(√x-2 ) = √7 (√7-2 )

Therefore, by considering the L.H.S and R.H.S,

it is understood that x=7

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