Task

You are going to use Excel to find solutions to equations.

You are trying to find solutions to equations involving x², x³, square, cube or higher power roots.

Examples:

What is the value of the x in the equation 2x²+3x-5=0
Or what is the value of x such that x⁵=100?

You are going to use the Excel program to help with this investigation.

Basic steps

Set up two columns. One for your (improving!) estimates of the value of x and the other for the value of the function generated by that value of x.

Now enter the formula for your function into cell B2

Examples

To square the value of x found in cell a2 use the formula:
=a2^2
and press return or enter.
The ^ symbol is obtained by holding shift down and typing 6.

To find the value of the function x³+2x²+1 for the value x found in cell a2 use the formula:
=a2^3+2*a2^2+1
and press return or enter.
The * symbol is obtained by holding shift down and typing 8. * is Excel for multiply.

Solving a problem.

You are going to use the spreadsheet to find a value of x such that:
x⁵=100

First type the formula into cell b2
=a2^5
and press return or enter.

Now copy this formula down the column by left clicking cell b2 to select it. Then right click on the corner of the cell, hold it down and drag down the column. This will copy your formula into the other cells in column b.

Now try to find the right value of x.
2 is too small it gives 32
3 is too big it give 243
2.5 is closer with a value of 97.6
2.512 is even better.

Challenges

1) Find a value of x such that x⁷=10000

2) Find a value of x such that x⁴+x³+x²=1000

3) Find a value of x such that x⁵+x³+x=1000

4) Find integer values (whole numbers) of x and y such that 11x+7y=1

5) Find values of x and y such that 15x+23y=5