Question

How do you find the real solutions of the equation by graphing `6x^2=48x`?

Answer 1

`x=0" and "x=8`

Explanation:

`color(blue)("Solving from the graph")`

Given:`" "6x^2=48x`

divide both sides by 6

`x^2=8x`

Subtract 8x from both sides

`x^2-8x=0`

Set as `y=x^2-8x` and plot the graph

Read of the values of `x` for which `y` is 0

Giving: `x=0" and "x=8`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solving using maths")`

Given that `x^2-8x=0`

`=>x^2=8x`

Divide both sides by `x`

`color(brown)(x=8 larr" First solution")`

Again consider `x^2=8x`

Known that 0 times any number gives 0

Let `x=0` giving

`x^2=8x" "->" "0xx0=8xx0" "->" "0=0 larr" True"`

`color(brown)("So "x=0 larr" Second solution")`