Let the two numbers be x and x - 4 Given that the difference of two numbers is 4. By the given hypothesis, we have `1/(x-4)-1/x=4/21` `rArr(x-x+4)/(x(x-4))=4/21` ⇒ 84 = 4x(x – 4) ⇒ 𝑥2 - 4𝑥 - 21 = 0 ⇒ 𝑥2 - 7𝑥 + 3𝑥 - 21 = 0 ⇒ 𝑥(𝑥 - 7) + 3(𝑥 - 7) = 0 ⇒ (𝑥 - 7)(𝑥 + 3) = 0 ⇒ 𝑥 = 7 𝑜𝑟 𝑥 = -3 and If x = -3, x – 4 = -3 - 4 = -7 Hence, required numbers are 3, 7 and -3, -7 > Solution Let the two numbers be x and y, given that, x- y =4 x = y + 4 -----(i) and From (i)
So, when y = 3; x = y+ 4 = 7 Or, when y = -7; x = y+ 4 = -3 Mathematics RD Sharma Standard X 2 |