Question

Two whole numbers a and b satisfy the following conditions find a and b a b = 30 a:b is equivalent to 2:3

Answer 1

Answer:

$a=2\sqrt5, b= 3\sqrt5$

Step-by-step explanation:

We are given that tow whole number a and b

ab=30

a:b=2:3

We have to find a and b.

$ab=30$

$\frac{a}{b}=\frac{2}{3}$

$a=\frac{2}{3}b$

Substitute the value of a

$\frac{2}{3}b\times b=30$

$\frac{2}{3}b^2=30$

$b^2=\frac{30\times 3}{2}=45$

$b=\sqrt{45}=\sqrt{3\times 3\times 5}=\pm3\sqrt5$

We take the value of positive because b is a whole number

Substitute the value of $b=3\sqrt 5$

$a=\frac{2}{3}\times 3\sqrt5=2\sqrt5$

Hence, $a=2\sqrt5, b= 3\sqrt5$