Question

guys pls tell the sol . this que is of calculus 11th​

Answer 1

56 as 8into 7 is equal to 56

Answer 2

Answer:

64

Explanation:

Given as

$\alpha + \beta = 16$

We have to find maximum value of

$\alpha \times \beta$

We know that from A.M, GM inequality .

$\frac{ \alpha + \beta }{2} \geqslant \sqrt{ab}$

$since \: \frac{16}{2} \geqslant \sqrt{ \alpha \beta } \\ \\ \alpha \beta \geqslant 8 {}^{2} \\ \\ \alpha \beta \leqslant 64$

Since , maximum value of

$\alpha \beta = 64$

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Alternative method(2)

$16{}^{2} = ( \alpha + \beta ) {}^{2} = \alpha {}^{2} + \beta {}^{2} + 2 \alpha \beta - - (1) \\ \\ 0 \leqslant ( \alpha - \beta ) {}^{2} = \alpha {}^{2} + \beta {}^{2} \ - 2 \alpha \beta - - (2) \\ \\ substract(2)from(1) \\ \\ we \: get \: \alpha \beta \leqslant \frac{256}{4} \leqslant \red{64} \pink{answer}$

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