Question

Hey i just got one doubt...why is (alpha-beta)²=(alpha+beta)²-4(alpha×beta)??why is there a 4 in it??pls tell ​

Answer 1

To prove:

• (α - β)² = (α + β)² - 4αβ

Considering L.H.S:

ㅤ=ㅤ(α - β)²

We know, (a - b)² = a² - 2ab + b².

ㅤ=ㅤα² - 2αβ + β²

Adding and Subtracting 2αβ.

ㅤ=ㅤα² - 2αβ + β² + 2αβ - 2αβ

Rearranging the terms.

ㅤ=ㅤα² + 2αβ + β² - 2αβ - 2αβ

We know, (a + b)² = a² + 2ab + b².

ㅤ=ㅤ(α + β)² - 2αβ - 2αβ

ㅤ=ㅤ(α + β)² - 4αβ

ㅤ=ㅤR.H.S

Hence,

• Proved.

Answer 2

Answer:

It is correct.

Why? look at the explanation :)

Step-by-step explanation:

Let alpha be "a", beta be "b"

$(a-b)^2 = (a+b)^2 - 4ab$

By Factorising by Algebraic Identities,

$a^2 + b^2 - 2ab = a^2 + b^2 + 2ab - 4ab$

Canceling out the common term,

$-2ab = 2ab-4ab$

$-2ab = -2ab$

LHS=RHS, it is verified

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