Question

(7sqrt(3))/(sqrt(10+sqrt(3)))-(2sqrt(5))/(sqrt(6)+sqrt(5))-(3sqrt(2))/(sqrt(5)+3sqrt(2))
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Answer 1

Solution :-

→ (7√3/√10 + √3) - (2√5/√6 + √5) - (3√2/√15 + 3√2)

Let,

• x = (7√3/√10 + √3)
• y = (2√5/√6 + √5)
• z = (3√2/√15 + 3√2)

so,

→ x = (7√3/√10 + √3)

rationalising the denominator,

→ x = 7√3 * (√10 - √3) / (√10 + √3)(√10 - √3)

→ x = 7√3 * (√10 - √3) / (10 - 3)

→ x = 7√3 * (√10 - √3) / 7

→ x = (√30 - 3)

now,

→ y = (2√5/√6 + √5)

rationalising the denominator,

→ y = 2√5 * (√6 - √5) / (√6 + √5)(√6 - √5)

→ y = 2√5(√6 - √5) / (6 - 5)

→ y = 2√30 - 2 * 5

→ y = (2√30 - 10)

and,

→ z = (3√2/√15 + 3√2)

→ z = 3√2 * (√15 - 3√2) / (√15 + 3√2)(√15 - 3√2)

→ z = 3√2(√15 - 3√2) / (15 - 18)

→ z = (-√2(√15 - 3√2)

→ z = (-√30 + 6)

then,

→ x - y - z

→ (√30 - 3) - (2√30 - 10) - (-√30 + 6)

→ √30 - 2√30 + √30 - 3 + 10 - 6

→ 2√30 - 2√30 + 10 - 9

→ 10 - 9

→ 1 (Ans.)

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Answer 2

Answer:

solution = 114-41 root 6 by 30