GCSE Maths Questions

Hi, ive been doing practice questions for maths and have been fine with all of them except these three and would be grateful if someone could show me how to do them
1) 4n^2/3=8^-1/3 Find the value of n

2) The diagram shows a sketch of the graph y=ab^x
The curve passes through the points A(0.5,1) and B(2,8)
The point C(-0.5,k) lies on the curve
Find the value of k



3)Solve 2x^2+8x-3=0
Give your answers in the form p+or- square root of q/r where p,q and r
are integers
This one has to be done by completing the square
Thankyou

Can you put some brackets in 1) as your notation is ambiguous?

2) Substitute your points into the equation and form a pair of simultaneous equations. Now how might you solve them to find the values of a and b?

3) It doesn't have to be done by completing the square (unless the question says so). You might find the quadratic formula easier.

Do you mean $4n^\frac{2}{3} =8^\frac{-1}{3}$

1) sorry, do you mean like this? 4n^(2/3) = 8^ -(1/3)

2) like this ? , 1=ab^0.5
8=ab^2

1=ab^ (1/2) = square root of ab
8=ab^2

7=ab^2 - square root of ab ?

I don't think i've done that right

3) it was in the completing the square part of the book so i presumed it had to be. I did this

x^2+4x-1.5=0
(x+2)^2 -2.5 =0
(x+2)^2 = 2.5
(x+2) = square root of 2.5
x = 2 +or- square root of 2.5

and then got stuck?

2) like this ?
1=ab^0.5
8=ab^2

Can we deal with them one at a time as this is getting confusing?

Let's start with 3) as you are close.

Second line of your working.

$-4-1.5 \neq -2.5$

oh so it would be (x+2)^2-5.5=0
x= -2 +or- square root of 5.5
x= -2 +or- square root of (11/2)

This is right. Now you don't want to SUBTRACT the equations, you want to DIVIDE the second by the first.

I've just noticed you are now solving a different question to the one you provided in your opening post. Which one is correct?

I halved the original question so i could use completing the square

Fair enough - I was being dim not to realise what you were doing.

You have ambiguous notation in your question again.

Is the square root supposed to apply to (q/r) or just to q?

I ask because I don't know whether you need to rationalise the denominator of your surd or not.

Nearly. What is $\displaystyle \frac{a}{a}$ when $a\neq 0$ ?

1?

8=ab^2
1=ab^0.5

can i cancel the a to make

8=b^(3/2) ?

the square root is meant to apply to (q/r)

Yes now square both sides and then cube root both sides to find b.

You can then substitute back into one of the original equations to find a.