> Solution Let the two natural numbers be x and y X+y=8 X=8-y ---(Equation-1) 1/x+1/y=8/15 ---(Equation -2) We get, 1/8-y+1/y=8/15 Y+8-y/-y2+8y=8/15 8/-y2+8y=8/15 120=-8y2+64y -8y2+64y=120 -8y2+64y-120=0 8y2-64y+120=0 y2-8y+15=0 y2-5y-3y+15=0 (sum=-8,Product=15) y(y-5)-3(y-5)=0 y-5=0 (or)y-3=0 y=5 (or) y=3 If y=5 then x=8-5 X=3 If y=3 then x=8-3 X=5 Therefore the two natural numbers are 3and 5 Suggest Corrections 0 Let the two numbers be x and y respectively.Then,x + y = 8 ….(i)⇒ x = 8 - yAnd, `1/x + 1/y = 8/15` ⇒ `[ y + x ]/[xy] = 8/15` ⇒ `8/(xy) = 8/15` .....[ From(1) ]⇒ xy = 15⇒ ( 8 - y )y = 15 ⇒ 8y - y2 = 15 ⇒ y2 - 8y + 15 = 0 ⇒ y2 - 3y - 5y + 15 = 0⇒ y( y - 3 ) - 5( y - 3 ) = 0⇒ ( y - 3 )( y - 5 ) = 0⇒ y = 3 or y = 5⇒ x = 5 or x = 3 Thus, the two numbers are 3 and 5 respectively. |