Question

If (28-x) is the mean proportional of (23-x) and (19-x) then find the value of x​

Answer 1

Answer:

x = 28

Step-by-step explanation:

(23-x) : (28-x) : : (28-x) : (19-x)

(23-x) × (28-x) = (28-x) × (19-x)

23 (28-x) - x (28-x) = 28 (19-x) - x (19-x)

(23×28 - 23×x) - (x×28 - x×x) = (28×19 - 28×x) - ( x×19 - x×x )

(644 - 23x) - (28x - x^2) = (532 - 28x) - (19x - x^2)

644 - 23x - 28x + x^2 = 532 - 28x - 19x + x^2

644 - 51x + x^2 = 532 - 47x + x^2

644 - 51x = 532 - 47x

644 - 532 = 51x - 47x

112 = 4x

x = 112 ÷ 4

x = 28

Answer 2

Answer:

347/14

Step-by-step explanation:

If a, b and c are in proportional:

    a/b = b/c     or ac = b²    

⇒ √ac = b

Where b is the mean proportional of a and c.

       Here,

⇒ √(23 - x )(19 - x) = (28 - x)

⇒ (23 - x)(19 - x) = (28 - x)²

⇒ 437 - 23x - 19x + x² = 784 + x² - 56x

⇒ 56x - 42x = 784 - 437

⇒ x = 347/14

  ∴ value of x is 347/14