Question

if the sum of two number is 14 and multiplication is 40 then find their difference​

Answer 1

Answer: difference=6 or -6

Step-by-step explanation:

let one no. be a

let another no. be b

a.t.q.,

⇒ a+b=14 ---------------------------(i)

⇒ a*b=40 ---------------------------(ii)

⇒ b=14-a

putting value of b in eq. (ii), we get,

⇒a*(14-a)=40

⇒14a-a²=40

⇒a²-14a+40=0

⇒a²-10a-4a+40=0

⇒a(a-10)-4(a-10)=0

⇒(a-4)(a-10)=0

so, a=4,10

            a+b=14                                            |                      a+b=14

            b=14-4                                            |                       b=14-10

            b=10                                                |                       b=4

now we will take values of a and b one by one=

            a-b=10-4=6      or        a-b=4-10=-6

Answer 2

Answer:

Step-by-step explanation:

Let the two numbers be x and y

Therefore x + y = 14

                     xy = 40

Let us square this equation

$(x + y)^{2} = x^{2} + y^{2} + 2xy$

  $14^{2} = x^{2} + y^{2} + 2(40)$

  $196 = x^{2} + y^{2} + 80\\196 - 80 = x^{2} + y^{2}\\116 = x^{2} + y^{2}$

Therefore,

$(x - y)^{2} = x^{2} + y^{2} - 2xy\\\(x - y)^{2} = 116 - 2(40)\\(x - y)^{2} = 116 - 80\\(x - y)^{2} = 36\\ x - y = \sqrt{36} \\ x - y = 6$

x - y = 6