Question

8. If (17 – X) is the mean proportional of (10 – x) and (31 - x), then find the value of x. (give only right ans with explanation)​

Answer 1

Step-by-step explanation:

Given :-

17 – X) is the mean proportional of

(10 – X) and (31 - X)

To find :-

The value of X

Solution :-

Given numbers are (10-X) and (31-X)

We know that

The mean proportional of the numbers a and b is √(ab)

The Mean Proportional of 10-X and 31-X

= √[(10-X)(31-X)]

= √(310-10X-31X+X²)

= √(310-41X+X²)

= √(X²-41X+310)

According to the given problem

The mean proportional = (17-X)

Therefore, √(X²-41X+310) = 17-X

On squaring both sides then

=>[√(X²-41X+310) ]² = (17-X)²

=> X²-41X+310 = 17²-2(17)(X)+X²

Since, (a-b)² = a²-2ab+b²

=> X²-41X+310 = 289-34X+X²

=> X²-X²-41X+34X = 289-310

=> -7X = -21

=> 7X = 21

=> X = 21/7

=> X = 3

Therefore, X = 3

Answer :-

The value of X is 3

Check :-

If X = 3 then the two numbers will be

10-3 = 7 and 31-3 = 28

Their mean proportional = √(7×28)

=√(196)

= 14

If X = 3 the 17-X = 17-3 = 14

Hence , Verified the given relations in the given problem.

Used formulae:-

→ The mean proportional of the numbers a and b is √(ab)