Question

a√a+b√b=183 and a√b+b√a=182 find 9÷5(a+b)

Answer 1

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$= > a \sqrt{a} + b \sqrt{b} = 183 \\ \\ or. \: \: {( \sqrt{a}) }^{3} + {( \sqrt{b} )}^{3} = 183 \\ \\ or. \: \: {( \sqrt{a} + \sqrt{b} )}^{2} - 3(a \sqrt{b} + b \sqrt{a)} ) = 183 \\ \\ or. \: \: {( \sqrt{a} + \sqrt{b} )}^{2} - 3 \times 182 = 18 3 \\ \\ or. \: \: \sqrt{a} + \sqrt{b} = \sqrt{183 + 182 \times 3} = \sqrt{183 + 546} \\ \\ or. \: \: \sqrt{a} + \sqrt{b} = \sqrt{729} = 27$
Now,
$= > a \sqrt{b} + b \sqrt{a} = 182 \\ \\ or. \: \: \sqrt{ab} ( \sqrt{a } + \sqrt{b} ) = 182 \\ \\ or. \: \: \sqrt{ab} \times 27 = 182 \\ \\ or. \: \: \sqrt{ab} = \frac{182}{27}$
So,
$= > a + b = {( \sqrt{a}) }^{2} + {( \sqrt{b} )}^{2} \\ \\ or. \: \: a + b \: = ( \sqrt{a} + \sqrt{b} )^{2} - 2 \sqrt{ab} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {27}^{2} - 2 \times \frac{182}{27} = 729 - \frac{364}{27}$
Thus,
$= > \frac{9}{5(a + b)} \\ \\ = \frac{9}{5(729 - \frac{364}{27} )} \\ \\ = \frac{9 \times 27}{5 \times 729 \times 27 - 364} \\ \\ = \frac{243}{98415 - 364} = \frac{243}{98051} = 0.0025$
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