Question

if 2√3-√5|4√3-3√5=x-√15y find x and y.​

Answer 1

Answer:

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Answer 2

Answer:

Required value of x is 13 and value of y is$3 \frac{1}{3}$

Step-by-step explanation:

Given,

$\frac{2 \sqrt{3} - \sqrt{5} }{4 \sqrt{3} - 3 \sqrt{5} } = x - \sqrt{15} y.....(1)$

Now,

$\frac{2 \sqrt{3} - \sqrt{5} }{4 \sqrt{3} - 3 \sqrt{5} } =\frac{(2 \sqrt{3} - \sqrt{5}) (4 \sqrt{3} - 3 \sqrt{5})}{(4 \sqrt{3} - 3 \sqrt{5})( 4 \sqrt{3} + 3 \sqrt{5})} =\frac{24 - 6 \sqrt{15} - 4 \sqrt{15} + 15}{ {(4 \sqrt{3)} }^{2} - {(3 \sqrt{5)} }^{2} } = \frac{39 - 10 \sqrt{15} }{3}$

From equation (1),

$\frac{39 - 10 \sqrt{15} }{3} = x - \sqrt{15} y$

$\frac{39}{3} - \frac{10}{3} \sqrt{15} = x - \sqrt{15} y$

We are comparing both side and get,

$x = \frac{39}{3} = 13$

and $y = \frac{10}{3} = 3 \frac{1}{3}$

Here applied formulas are,

$1.{x}^{2} - {y}^{2} = (x + y)(x - y) \\ 2. \sqrt{x} \times \sqrt{x} = x \\ 3. \sqrt{x} \times \sqrt{y} = \sqrt{xy}$

Some other important formulas of power of indices,

$1.{x}^{0} = 1 \\ 2.{x}^{1} = x \\ 3.{x}^{a} \times {x}^{b} = {x}^{a + b} \\ 4.\frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ 5. {x}^{ {y}^{a} } = {x}^{ya} \\ 6.{x}^{ - 1} = \frac{1}{x} \\ 7. {x}^{a} \times {y}^{a} = {(xy)}^{a}$