Question

3 pts 64. एक संख्या को 4 से भाग देने पर भागफल तथा शेषफल का योग 8 है तथा उनके वर्गों का योग 34 है, वह संख्या ज्ञात कीजिए।

Answer 1

Answer:

Number is 23

Step-by-step explanation:

let quotient (भागफल) = x

remainder (शेषफल) = y

from question,

x + y = 8       -------------- (i)

x² + y² = 34  -------------- (ii)

Now,

(x + y)² = x² + y² + 2xy

(8)² = 34 + 2xy

64 -34 = 2xy

2xy = 30  -------------------- (iii)

Again,

(x - y)² = x² + y² - 2xy

(x - y)² = 34 - 30      [ from equation (ii) and (iii) ]

(x - y) = √4

x - y = 2  ----------------------- (iv)

Now add equation (i) and (iv)

(x + y) + (x - y) = 8 + 2

x + y + x - y = 10

2x = 10

x = 5

put x = 5 in equation (i)

5 + y = 8

y = 8 - 5 = 3

so, x = 5 and y = 3

Number = (divisor x quotient) + remainder

संख्या = ( भाजक x भागफल ) + शेषफल

         = ( 4 x 5 ) + 3

         = 20 + 3 = 23