Math, asked by cutepori18, 4 months ago


When x is subtracted from each of 21, 22, 60 and 64, the numbers so
obtained, in this order, are in proportion. What is the mean proportional
between (x+1) and (7x+8)?​

Answers

Answered by ayushishrivastava81
0

Step-by-step explanation:

Given numbers are 21,22,60 and 64

Now, x is subtracted from the number

So, (21-x) :(22-x):: (60-x):(64-x)

(22-x) (60-x) =(21-x) (64-x)

X= 8

Mean proportion of (x+1) &(7x+8)

= 24

Answered by tennetiraj86
2

Step-by-step explanation:

Given:-

When x is subtracted from each of 21, 22, 60 and 64, the numbers so obtained, in this order, are in proportion.

To find:-

What is the mean proportional between (x+1) and (7x+8)?

Solution:-

Given numbers are 21 ,22 ,60, 64.

If x is subtracted from the each of the numbers then they are in proportion.

(21-x) , (22-x) , (60-x) and (64-x) are in proportion.

Means = (22-x) and (60-x)

Product of means = (22-x)(60-x)

=>22(60-x)-x(60-x)

=>1320-22x-60x+x^2

=>1320 -82x +x^2

Product of means = x^2-82x +1320

Extremes = (21-x) and (64-x)

Product of extremes = (21-x)(64-x)

=>21(64-x)-x(64-x)

=>1344-21x-64x+x^2

=>1344-85x+x^2

Product of extremes = x^2 -85x +1344

We know that

In proportion ,

The product of extremes = The Product of means

=>x^2-82x +1320 = x^2 -85x +1344

On cancelling x^2 both sides then.

=>-82x +1320 = -85x +1344

=>-82x+85x = 1344-1320

=>3x = 24

=>x = 24/3

=>x = 8

The value of x = 8

Now,

x+1 = 8+1 = 9

7x+8=7(8)+8=56+8= 64

We know that

The mean Proportional of a and b is √(ab)

We have a = 9 and b = 64

Mean Proportional of 9 and 64 =

=>√(9×64)

=>√576

=>24

Answer:-

Mean Proportional of x+1) and (7x+8) is 24

Used formulae:-

1)

In proportion ,

The product of extremes = The Product of means

2)The mean Proportional of a and b is √(ab)

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