Question

Formulae for alpha square plus beta square

Answer 1

Hi there !

α² + β² = (α + β)² - 2αβ 
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Here are some other important formulas which can be useful for you :-

(α + β)² = (α - β)² + 4αβ
(α - β)² = (α + β)²  - 4αβ
α³ + β³ = (α + β)³ - 3αβ [ α + β ]
α⁴ + β⁴ = (α² + β²)² - 2α²β²

Answer 2

$\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha \beta$

$\alpha^2+\beta^2=(\alpha+\beta)^2+2\alpha \beta$

Step-by-step explanation:

To find : The formula for $\alpha^2+ \beta^2$ ?

Solution :

We know the algebraic identity,

$(\alpha+\beta)^2=\alpha^2+\beta^2+2\alpha \beta$

Re-write as,

$\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha \beta$

Using another algebraic identity,

$(\alpha-\beta)^2=\alpha^2+\beta^2-2\alpha \beta$

Re-write as,

$\alpha^2+\beta^2=(\alpha+\beta)^2+2\alpha \beta$

Therefore,

$\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha \beta$

$\alpha^2+\beta^2=(\alpha+\beta)^2+2\alpha \beta$

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Formula for alpha square minus beta square

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