Show that x satisfies the equation

Question

The surface area, A cm^{2 ,} of a prism is given by the formula A = 12x² + 12Lx.

E = 98 cm

A = 448 cm

Formulae for L is: L =1/3(E - 24x)

 

Substitute the values E and A into the formulae L and A to show that x satisfies the equation 3x² - 14x + 16 = 0.

 

Please can you expain how you found the solution. Thank you.

Answer 1

You have to do exactly what it says, substitute the values for E and A

 

A = 12x²+12Lx

L = 1/3 (E-24x)

 

If E = 98

L = 1/3 (98-24x)

L = 98/3 - 8x

 

A = 12x² + 12Lx

 

If A = 448

448 = 12x²+12Lx

Factor out 12x

448 = 12x(x+L)

 

Since L = 98/3 - 8x

448 = 12x[x + (98/3 - 8x)]

448 = 12x[98/3-7x]

448 = 392x - 84x²

84x²-392x+448 = 0

Factor out 28

3x²-14x+16 = 0