Value of [tex]x[/tex]is [tex] - 12[/tex].
Final Answer is [tex]480[/tex]
Step-by-step explanation:
Assume that:
First number = x
Second number = 20 - x
Putting the given conditions,
[tex]2x^{2} + 3(20 - x)^{2} [/tex]
Putting the formula (a-b)²=(a²+2ab+b²) in (20-x)²,
[tex]2 {x}^{2} + 3(20^{2} - 2 \times 20 \times x + {x}^{2})[/tex]
[tex] = > 2 {x}^{2} + 3(400 - 40x + x^{2})[/tex]
Opening the brackets,
[tex]2 {x}^{2} + 3 \times 400 - 3 \times 40x + 3 \times {x}^{2} [/tex]
[tex] = > 2 {x}^{2} - 1200 - 120x + 3{x}^{2}[/tex]
[tex] = > (2x^{2} + 3 {x}^{2}) - 120x + 1200[/tex]
[tex] = > 5 {x}^{2} - 120x + 1200[/tex]
[tex]As \: x= - \frac{b}{2a}[/tex]
[tex] = > - \frac{120}{2 \times 5}[/tex]
[tex] = > - \frac{120}{10} [/tex]
[tex] = > - 12[/tex]
Now substituting the value of x in 5x²-120x+1200,
[tex] = > (5 \times {12}^{2} )-(120 \times 12)+1200[/tex]
[tex] = > (5 \times 144)-(1440)+1200[/tex]
[tex] = > 720 - 1440 + 1200[/tex]
[tex] = > 720 - (1440 - 1200)[/tex]
[tex] = > 720 - 240[/tex]
[tex] = > 480[/tex]
