If 2-5 -2-5-x and 2-5 -2-5-y - find the value of x2-y2

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Byju's Answer

Standard XII

Mathematics

Domain

If 2+√5 ÷2-√5...

Question

If (2 + √5) ÷ (2 - √5) = x and (2 - √5) ÷ (2 + √5) = y; find the value of x² - y²

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Solution

Dear student

x = 2-√5/2+√5
on rationalization

x = (4 + 5 – 4 √5) / – 1

x = 4 √5 – 9

Now similarly y = – 4 √5 – 9

Now question is asked for x^2 – y^2
= (x+y) * (x – y)

= – 18 * 8 √5
= – 144√5

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If (2 + √5) ÷ (2 - √5) = x and (2 - √5) ÷ (2 + √5) = y; find the value of x​​​​​​2 - y​​​​​​2

Dear student x = 2-√5/2+√5 on rationalization x = (4 + 5 – 4 √5) / – 1 x = 4 √5 – 9 Now similarly y = – 4 √5 – 9 Now question is asked for x^2 – y^2 = (x+y) * (x – y) = – 18 * 8 √5 = – 144√5

If (2 + √5) ÷ (2 - √5) = x and (2 - √5) ÷ (2 + √5) = y; find the value of x² - y²

Dear student

x = 2-√5/2+√5
on rationalization

x = (4 + 5 – 4 √5) / – 1

x = 4 √5 – 9

Now similarly y = – 4 √5 – 9

Now question is asked for x^2 – y^2
= (x+y) * (x – y)

= – 18 * 8 √5
= – 144√5