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Some important expressions

July 22, 2020
Category: Some important expressions

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☼ Some important expressions :– We know that,

$\alpha + \beta = - \frac{b}{a}$ & $\alpha \beta = \frac{c}{a}$

(i) $\alpha$ ² + $\beta$ ² = ( $\alpha$ + $\beta$ )² – 2 $\alpha$ $\beta$

(ii) ( $\alpha$ – $\beta$ )² = ( $\alpha$ + $\beta$ )² – 4 $\alpha$ $\beta$ $\large \Rightarrow$ $\alpha$ – $\beta$ = $\pm \sqrt{\left (\alpha + \beta \right )^{2}- 4\alpha\beta}$

(iii) $\alpha$ ³ + $\beta$ ³ = ( $\alpha$ + $\beta$ )³ – 3 $\alpha$ $\beta$ ( $\alpha$ + $\beta$ )

(iv) First find $\alpha$ – $\beta$ , then $\alpha$ ³ – $\beta$ ³ = ( $\alpha$ – $\beta$ )³ + 3 $\alpha$ $\beta$ ( $\alpha$ – $\beta$ )

(v) First find $\alpha$ ² + $\beta$ ², then $\alpha$ ⁴ + $\beta$ ⁴ = ( $\alpha$ ² + ²)² – 2 $\alpha$ ² $\beta$ ²

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Some important expressions

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