Question

How do I solve this?

Answer 1

Value of
`x`is
`- 12`.

Final Answer is
`480`

Explanation:

Assume that:

First number = x

Second number = 20 - x

Putting the given conditions,

`2x^(2) + 3(20 - x)^(2)`

Putting the formula (a-b)²=(a²+2ab+b²) in (20-x)²,

`2 {x}^(2) + 3(20^(2) - 2 * 20 * x + {x}^(2))`

`= > 2 {x}^(2) + 3(400 - 40x + x^(2))`

Opening the brackets,

`2 {x}^(2) + 3 * 400 - 3 * 40x + 3 * {x}^(2)`

`= > 2 {x}^(2) - 1200 - 120x + 3{x}^(2)`

`= > (2x^(2) + 3 {x}^(2)) - 120x + 1200`

`= > 5 {x}^(2) - 120x + 1200`

`As \: x= - (b)/(2a)`

`= > - (120)/(2 * 5)`

`= > - (120)/(10)`

`= > - 12`

Now substituting the value of x in 5x²-120x+1200,

`= > (5 * {12}^(2) )-(120 * 12)+1200`

`= > (5 * 144)-(1440)+1200`

`= > 720 - 1440 + 1200`

`= > 720 - (1440 - 1200)`

`= > 720 - 240`

`= > 480`