Question

x और y ऐसी दो संख्याएँ हैं जिनका माध्य
अनुपात 16 है और तृतीय अनुपात 128 है।।
xऔर y का मान क्या है?
​

Answer 1

SOLUTION

GIVEN

x and y are two numbers such that mean proportion is 16 and third proportion is 128

TO DETERMINE

The value of x and y

EVALUATION

Here the given numbers are x and y

Now third proportion is 128

So we have

x : y = y : 128

$\displaystyle \sf \implies \: \frac{x}{y} = \frac{y}{128}$

$\displaystyle \sf \implies \: {y}^{2} = 128x \: \: \: \: \: - - - - (1)$

Again mean proportion is 16

So we have

$\sf \: \sqrt{xy} = 16$

$\displaystyle \sf \implies \: xy = {16}^{2}$

$\displaystyle \sf \implies \: \frac{ {y}^{2} }{128} . y = {16}^{2}$

$\displaystyle \sf \implies \: \frac{ {y}^{3} }{128} = {16}^{2}$

$\displaystyle \sf \implies \: {y}^{3} = {16}^{2} \times 128$

$\displaystyle \sf \implies \: {y}^{3} = 16 \times 16 \times 128$

$\displaystyle \sf \implies \: {y}^{3} = 16 \times 16 \times 16 \times 8$

$\displaystyle \sf \implies \: {y}^{} = \sqrt[3]{ 16 \times 16 \times 16 \times 8}$

$\displaystyle \sf \implies \: y = 16 \times 2$

$\displaystyle \sf \implies \: y = 32$

From Equation 1 we get

$\displaystyle \sf {y}^{2} = 128x$

$\displaystyle \sf \implies \: {32}^{2} = 128x$

$\displaystyle \sf \implies \: 128x = 32 \times 32$

$\displaystyle \sf \implies \: x = 8$

FINAL ANSWER

x = 8 , y = 32

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ find the Geometric mean (G.P)between 1/9 and 729....

https://brainly.in/question/38105729

2. If x is a geometric mean of 16 & 4 then find value of x .

https://brainly.in/question/39297607

Answer 2

Answer :-

→ माध्य अनुपात = √(xy)

→ 16 = √(xy)

→ 256 = xy

→ x = (256/y) -------- (1)

अब,

→ तृतीय अनुपात = 128

→ y² = x * 128

→ y² = 128x --------- (2)

अत, (1) का मान (2) में रखने पर,

→ y² = 128 * (256/y)

→ y³ = 128 * 256

→ y = 32

इसलिए,

→ x = 256/32 = 8

x का मान 8 और y का मान 32 होगा ll

यह भी देखें :-

Consider the sequence defined by ak=1/k2-k for k ≥ 1. Given that aM + aM + 1 + …………+ aN – 1=1/29 for positive integers M...

https://brainly.in/question/42384271

(c)

75. From a number M subtract 1. Take the reciprocal of

the result to get the value of 'N'. Then which of the

followi...

https://brainly.in/question/39499253