Question

7) If a,b are the roots of x²-3x+1=0, then a²-b²=

Answer 1

$\underline{\underline{\green{\mathfrak{Answer:-}}}}$

C) 3√5

$\underline{\underline{\green{\mathfrak{Explanation:-}}}}$

Given

α,β are the roots of x²-3x+1 = 0

To Find

α²-β² = ??

Solution

As we know

Sum of the zeros(α+β) = $\dfrac{-b}{a}$

α+β = $\dfrac{-(-3)}{1}$

$\boxed{\alpha + \beta= 3}$

Also,

Difference of the roots(α-β) = $\dfrac{\sqrt{D}}{a}$

α-β = $\dfrac{\sqrt{{b}^{2}-4ac}}{a}$

α-β = $\dfrac{\sqrt{{(-3)}^{2}-4(1)(1)}}{1}$

α-β = $\sqrt{9-4}$

$\boxed{\alpha- \beta = \sqrt{5}}$

Let us, find α²-β²

= α²-β²

= (α+β)(α-β)

= (3)(√5)

= 3√5