Question

pls solve it
it's urgent
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Answer 1

Answer:

I think the ans is 0

please check it

Answer 2

Hence, the value of x^2 + y^2 - 34 is 0.

Step-by-step explanation:

Given:-

x = (√2 + 1)/(√2 - 1)

and

y = (√2 - 1)/(√2 + 1)

To find out:-

Value of x^2 + y^2 - 34

Solution:-

Concept:- First we rationalis the denominator x value and y value one by one. &

Second in question given we have to value of x^2 + y^2 - 34, so here we will so same thing put Reqd values of x and y. The last we will get the final answer.

Let's solve,

We have

x = (√2 + 1)/(√2 - 1)

The denomination = √2-1

We know that

Rationalising factor of √a - b = √a + b

So, rationalising factor of √2-1 = √2+1.

On rationalising the denominator them

x = [(√2+1)/(√2-1)] × [(√2+1)/(√2+1)]

x = [(√2+1)(√2+1)]/[(√2-1)(√2+1)]

Now, applying algebraic Identity in denominator because it is in the form of: (a-b)(a+b) = a^2 - b^2

Where, we have to put a = √2 and b = 1, we get

x = [(√2+1)(√2+1)]/[(√2)^2 + (1)^2]

x = [(√2+1)(√2+1)]/(2 - 1)

x = [(√2+1)(√2+1)]/1

x = (√2+1)(√2+1)

Now, applying algebraic Identity because this expression in the form of (a+b)(a+b) = (a+b)^2 = a^2+2ab+b^2

Where, we have to put in our expression a = √2 and b = 1, we get

x = (√2+1)^2

x = √2 + 2(√2)(1) + (1)^2

x = 2 + 2√2 + 1

x = 3 + 2√2

Similarly,

y = (√2 - 1)/(√2 + 1)

The denomination = √2+1

We know that

Rationalising factor of √a+ b = √a - b

So, rationalising factor of √2+1 = √2-1.

On rationalising the denominator them

y = [(√2-1)/(√2+1)] × [(√2-1)/(√2-1)]

y = [(√2-1)(√2-1)]/[(√2+1)(√2-1)]

Now, applying algebraic Identity in denominator because it is in the form of: (a+b)(a-b) = a^2 - b^2

Where, we have to put a = √2 and b = 1, we get

y = [(√2-1)(√2-1)]/[(√2)^2 + (1)^2]

y = [(√2-1)(√2-1)]/(2 - 1)

y = [(√2-1)(√2-1)]/1

y = (√2-1)(√2-1)

Now, applying algebraic Identity because this expression in the form of (a-b)(a-b) = (a-b)^2 = a^2-2ab+b^2

Where, we have to put in our expression a = √2 and b = 1, we get

y = (√2-1)^2

y = √2 - 2(√2)(1) + (1)^2

y = 2 - 2√2 + 1

y = 3 - 2√2

∴ x^2 + y^2 - 34

→ (3+2√2)^2 +(3-2√2)^2 - 34

→ 9 + 8 + 12√2 + 9 + 8 - 12√2 - 34

12√2 will cancel out.

→ 9 + 8 + 9 + 8

→ 34 - 34

→ 0.

Answer:-

Hence, the value of x^2 + y^2 - 34 is 0.

Used formulae:-

Rationalising factor of √a - b = √a + b

Rationalising factor of √a+ b = √a - b

(a-b)(a+b) = a^2 - b^2

(a+b)(a-b) = a^2 - b^2

(a+b)(a+b) = (a+b)^2 = a^2+2ab+b^2

(a-b)(a-b) = (a-b)^2 = a^2-2ab+b^2

:)