Question

Hola Brainliacs!!
Please help me find the answer of these questions (^^)
Q1. The product of two numbers is 144 and their sum is 24. What are the two numbers?
Q2. factorise
${2x}^{2} - 24x + 72$
Thanx!!

Answer 1

1 let the numbers be x and y
x+y=24
x=24-y
xy =144
24-y*y=144

24y-y^2=144
y^2-24y+144=0
y^2-12y-12y+144
y(y-12)-12(y-12)
y=12
x=24-y
c
x=24-12=12

Answer 2

(1)

Let the two numbers be x and y.

Given that product of two numbers is 144.

= > x * y = 144 ---- (1)

Given that sum of two numbers is 24.

= > x + y = 24

= > x = 24 - y ---- (2)

Now,

Substitute (2) in (1), we get

= > (24 - y) * y = 144

= > 24y - y^2 = 144

= > -y^2 + 24y - 144 = 0

= > y^2 - 24y + 144 = 0

= > y^2 - 12y - 12y + 144 = 0

= > y(y - 12) -12(y - 12) = 0

= > (y - 12)(y - 12) = 0

= > (y - 12)^2 = 0

= > y - 12 = 0

= > y = 12.

Now,

Substitute y = 12 in (1), we get

= > x * y = 144

= > x * 12 = 144

= > x = 144/12

= > x = 12.

Therefore, the two numbers are 12 and 12.

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(2)

Given Equation is 2x^2 - 24x + 72

= > 2(x^2 - 12x + 36)

= > 2(x^2 - 6x - 6x + 36)

= > 2(x(x - 6) - 6(x - 6))

= > 2(x - 6)(x - 6)

= > 2(x - 6)^2.

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Hope this helps!