Question

If x=root7+root6 ÷root7-root6 and y=root7-root6÷root7+root6 find x+y

Answer 1

Answer:

26

Step-by-step explanation:

x+y=7½+6½/7½-6½ +7½-6½/7½+6½

=[(7½+6½)²+(7½-6½)]/7-6

=(7+6+2.7½.6½+7+6-2.7½.6½)/1

=7+6+7+6

x+y=26

I think the answer is correct

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Answer 2

x=√(7)  + √(6)  ÷ √(7)  - √(6)

y=√(7) - √(6) ÷ √(7) + √(6)

∴ x=√(7)  + √(6)  ÷ √(7)  - √(6)

(Rationalize the denominator )

⇒ (√7 + √6) ÷ (√(7)  - √(6) ) × (√(7)  - √(6) ) ÷ (√(7)  - √(6) )

⇒  (√7 + √6) ² ÷ √(7)² - √(6)²

⇒ { (√7)² + 2 × √7 × √6 + (√6)² } ÷ 7 - 6

[∵ square cancle the squareroot so, (√7)² = 7 and (√6)² = 6]

⇒ { 7 + 2√42 + 6 } ÷ 1

⇒ 7 + 6 + 2√42

[∴ value of 1 in divide is nothing like 4 ÷ 1 = 4 ]

⇒ 13 + √84

∴ x = 13 + √84

Then, y = √(7) - √(6) ÷ √(7) + √(6)

(Rationalize the denominator )

⇒ (√7 - √6) ÷ (√7  + √6 ) × (√7  - √6 ) ÷ (√7  - √6 )

⇒ ( √7 - √6 )² ÷ (√7)² - (√6)²

[∵ square cancle the squareroot so, (√7)² = 7 and (√6)² = 6 ]

⇒  { (√7)² - 2 × √7 × √6 + (√6)² } ÷ 7 - 6

⇒ { 7 - 2√42 + 6 } ÷ 1

[∴ value of 1 in divide is nothing like 4 ÷ 1 = 4 ]

⇒ { 7 + 6 - √84}

⇒ 13 - √84

∴ y = 13 - √84

∴ x + y = ( 13 + √84 ) + (13 - √84)

[∵x + y = ( 13 + √84 ) + (13 - √84) ] is Answer