Question : The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two numbers becomes 260. Find the numbers.
Doubt by CBSE
Solution :
Let the first number be x
and the second number be (34-x)
ATQ
(x-3)(34-x+2)=260
(x-3)(36-x)=260
x(36-x)-3(36-x)=260
36x-x²-108+3x=260
-x²+39x-108=260
0=x²-39x+108+260
0=x²-39x+368
x²-39x+368=0
x²-(23+16)x+368=0
x²-23x-16x+368=0
x(x-23)-16(x-23)=0
(x-16)(x-23)=0
x-16=0 OR x-23=0
x=16 OR x=23
When x=16 then
First No. = x = 16
Second No. = 34-x = 34-16 = 18
When x=23 then
First No. = x = 23
Second No. = 34-x = 34-23 = 11
Hence, the required two numbers are 16 & 18 OR 23 & 11.