How do you solve $2 \sqrt{x} - 3 \sqrt{y} = 5$ $2sqrtx- 3 sqrty=5$ and $3 \sqrt{x} + 5 \sqrt{y} = 17$ $3 sqrtx+5sqrty=17$ ?

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Answer 1 · 2016-09-06T18:04:09

the soln. is $x = 16, y = 1$ $x=16, y=1$ .

$2sqrtx-3sqrty=5 ..........(1), &, 3sqrtx+5sqrty=17.................(2)$

$:. (1)xx5+(2)xx3$ , gives,

$10sqrtxcancel(-15sqrty)+9sqrtx+cancel(15sqrty)=51+25$ .

$:. 19sqrtx=76 rArr sqrt x=4 rArr x=16$ .

Then, by $(1), 2sqrt16-5=3sqrty rArr sqrty=1 rArr y=1$

These roots satisfy the given eqns.

Hence, the soln. is $x=16, y=1$ .

How do you solve 2sqrtx- 3 sqrty=52√x−3√y=52sqrtx- 3 sqrty=5 and 3 sqrtx+5sqrty=173√x+5√y=173 sqrtx+5sqrty=17?