Question

Mathematics : Equations. ​

Answer 1

• D)-2root5 is Answer

• refer attachment for detailed answer

• modified answer,, due to some mistakes

Answer 2

Answer:

Question :-

• If α and β are the roots of x² = x + 1, then find the value of α^2/β - β^2/α.

Given :-

• If α and β are the roots of x² = x + 1.

Find Out :-

• Find the value of α^2/β - β^2/α.

Solution :-

➙ x² = x + 1

➙ x² - x - 1 = 0

As it is given that the roots of this equation are α, β, we can, by the use of the sum and product of roots formulae, say that,

✭ Sum of two roots :-

➙ α + β = -(-1)/1 = 1

✭ Product of two roots :-

➙ αβ = -1

Now, we are asked to find the value of

➙ α^2/β - β^2/α

➙ (α^3 - β^3) / αβ

➙ (α - β)(α^2 + αβ + β^2) / -1

➙ -√[(α + β)^2 - 4αβ] [(α + β)^2 - αβ]

➙ -√[1 - 4(-1)] (1 - (-1))

➙ -2√5

Henceforth, the value of α^2/β - β^2/α is -2√5 .

Correct options is (d) - 2√5 .

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