Question

a+√b= 19
√a +b =13
Find the value of A and B

Answer 1

$\textbf{\huge{ANSWER:}}$

We can solve this question by the trial and error method. As the results are whole numbers, this tells us that the value of the numbers will be perfect square roots. Since we have both the results ( 13 and 19 ) below 20, we will take the perfect square roots of numbers under 20.

The perfect under roots under 20 are:
4 , 9 , and 16

Let's put these one by one:
First try:
a = 4
b = 16
$4 + \sqrt{16} = 4 + 4 = 8$

But 8 is not equal to 19. Thus, 4 and 16 are not the perfect pairs.

Second try:
a = 16
b = 9
$16 + \sqrt{9} = 16 + 3 = 19$
This pair satisfies the first equation. Now, let's put the same values in the second equation.
$\sqrt{16} + 9 = 4 + 9 = 13$
This pair even satisfies the second equation.

This means that this is the answer.

$\textbf{\huge{ a = 16 , b = 9}}$

Hope it Helps!! :)