Question

if a = root2+1 find the value of (a-1/a)2

Answer 1

Heya !!!



A = ✓2 + 1


Therefore,


1/A = 1/✓2+1


Rationalizing the denominator ✓2+1 we get,

1/A = 1/✓2 +1 × ✓2-1/ ✓2-1 = (✓2-1)/(✓2+1)(✓2-1) = (✓2-1)/(✓2)² - (1)²


1/A = (✓2-1)/2-1 = ✓2-1


Therefore,


A - 1/A = (✓2+1) - (✓2-1) = ✓2 +1 - ✓2 + 1 = 2



(A-1/A)² = (2)² = 4


Hence,


(A-1/A)² = 4




HOPE IT WILL HELP YOU....... :-)

Answer 2

Concept

A mathematical expression known as an algebraic expression is made up of mathematical operations, constants, and variables (addition, subtraction, multiplication, division). Terms are the components of algebraic expressions. Constants, coefficients, and unknown variables are used to represent these expressions.

Given

a = √2 ₊ 1

Find

we asked to find the value of (a ₋1/a)²

Solution

Given the value is a=√2 ₊ 1

Therefore, (a ₋1/a)² = [( √2 ₊ 1) ₋ 1/(√2 ₊ 1)]

here we have, 1/a = 1/(√2 ₊ 1)

to get a whole value we rationalize the given value.

1/a = 1/√2 ₊ 1 × √2 ₋ 1/√2 ₋ 1

     = (√2 ₋ 1) / (√2)² ₋ (1)²

     =  (√2 ₋ 1) / 1

∴ 1/a = √2 ₋ 1

Now substitute the value in the expression.

(a ₋1/a) = ( √2 ₊ 1 ) ₋ ( √2 ₋ 1)

            = √2 ₊ 1 ₋ √2 ₊ 1

            = 2

hence, (a ₋1/a)² = (2)²

           (a ₋1/a)² = 4

As a result, we determine that (a ₋ 1/a)² equals 4.

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