Question

1)(√7+√6/√7-√6)-2*√6*√7 2)(√5/√5+√2)+(√2/√5-√2)-10

Answer 1

..........................

Answer 2

Let's simplify each of these expressions step by step:

1. (√7+√6)/(√7-√6) - 2√6√7

To simplify the expression, we can use the conjugate pair to rationalize the denominator:

(√7+√6)/(√7-√6) * (√7+√6)/(√7+√6)

Now, we can multiply the numerators and denominators:

= [(√7 + √6) * (√7 + √6)] / [(√7 - √6) * (√7 + √6)] - 2√6√7

= [(√7 + √6)^2] / [(√7^2 - √6^2)] - 2√6√7

= [7 + 2√42 + 6] / [7 - 6] - 2√6√7

= (13 + 2√42) - 2√6√7

= 13 + 2√42 - 2√42

= 13

So, the first expression simplifies to 13.

2. (√5/(√5+√2)) + (√2/(√5-√2)) - 10

To simplify this expression, we can first find a common denominator:

= [√5(√5-√2) + √2(√5+√2)] / (√5+√2) - 10

Now, let's expand the numerators:

= [√5√5 - √5√2 + √2√5 + √2√2] / (√5+√2) - 10

= (5 - √10 + √10 + 2) / (√5+√2) - 10

Notice that the √10 terms cancel out:

= (5 + 2) / (√5+√2) - 10

= 7 / (√5+√2) - 10

To eliminate the radicals in the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator:

= (7 / (√5+√2)) * ((√5-√2)/ (√5-√2)) - 10

= (7(√5-√2)) / (5 - 2) - 10

= (7√5 - 7√2) / 3 - 10

Now, you can combine the fractions:

= (7√5 - 7√2)/3 - 10

So, the second expression simplifies to (7√5 - 7√2)/3 - 10.