If , are two real numbers satisfying ^2 + ^2 = 5 and 3( ^5 + ^5) … - Vidyadip

MCQ

If $\alpha , \beta $ are two real numbers satisfying $\alpha^2 + \beta^2$ = $ 5$ and $3(\alpha^5 + \beta^5) = 11$$(\alpha^3 + \beta^3)$, then $\alpha \beta$ is

✓
$2 $
B
$1$
C
$7$
D
$9$

✓

Answer

Correct option: A.

$2 $

a
$\frac{\left(\alpha^{5}+\beta^{5}\right)}{\left(\alpha^{3}+\beta^{3}\right)}=\frac{11}{3}$

$\frac{1}{\left(\alpha^{2}+\beta^{2}-\alpha \beta\right)}\left(\alpha^{4}+\beta^{4}-\alpha \beta\left(\alpha^{2}+\beta^{2}-\alpha \beta\right)\right)=\frac{11}{3}$

$\frac{\left(\alpha^{4}+\beta^{4}\right)}{\left(\alpha^{2}+\beta^{2}-\alpha \beta\right)}-\alpha \beta=\frac{11}{3}$

$\frac{25-2(\alpha \beta)^{2}}{5-\alpha \beta}-\alpha \beta=\frac{11}{3}$

Let $\alpha \beta=\mathrm{t} ;$ by cofficient $\alpha \beta=2$

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