Question

three numbers are in ratio of 2:3:5.given that the product of the extremes is 90find the difference between largest and smallest of them

Answer 1

Answer:

$\pm 9$

Step-by-step explanation:

$Three numbers are in the ratio \ 2:3:5. \\ \\ Let the three numbers be \ 2x,\ 3x\ and \ 5x. \\ \\ Difference between \ 5x\ and \ 2x\ is \ 5x - 2x = 3x,\ i.e., the middle term. \\ \\ Let's find the value of \ x. \\ \\ Given that, the product of the extremes, i.e., the product of the smallest and the largest terms, is 90.$

$\therefore\ (2x) \times (5x) = 90 \\ \\ = 10x^2 = 90 \\ \\ x^2 = 90 \div 10 = 9 \\ \\ x = \sqrt{9} = \pm 3$

$\therefore\ 3x = 3 \times \pm 3 = \pm 9 \\ \\ \therefore\ The difference is \ \pm 9.\ But if the question asks only about the difference from the largest to the smallest, then the answer will be 9 only. \\ \\ \\ Hope this may be helpful. \\ \\ Thank you. Have a nice day. \\ \\ \\ \#adithyasajeevan$

Answer 2

2x^2+3x^2+5x^2 =10^2

10x^2 = 90

x^2=9

x= √9

x = 3

then we have to multiply 2 3 5 with 3

6,9,15

the the difference is 15-9

=9