What is 4(2+3x)to the power of 1/2 + 3(2 + 3x) to the power of 3/2?

Question

Please explian how you slove the answer step by step

Answer 1

On a graphing calculator I got an answer of 40.08. On paper, though it is rather hard. Distribute first, so, = (8+12x^1/2)+(6+9x^3/2).
Solve in parenthesis to get, = (13.2+12x)+(26.9+9x). From there I'm lost, but calculators don't lie, so yeah. Good luck though.

Answer 2

Without a value for 'x' this cannot give a numerical answer, so the solution will be general. Also, the usual laws of indices do not help.

The way I would solve this is to use a binomial expansion for the terms in brackets being raised to a power.

By rewriting the brackets in the form of (1 + x) raised to a power it is possible to write the expansion fairly easily. A little further algebra (approx of A level standard) will give an asnwer containing 6 terms, 4 of which include powers of x. The problem is trying to write the solution using this type of word editor - so I'm not going to try - sorry!

Answer 3

The equation
4(2+3x)^1/2 + 3(2 + 3x)^3/2 = 0

Steps:
2 ((2+3x)^1/2) + 3^3/2 (2+3x)^3/2 = 0

((2+3x)^1/2) (2 + 3^3/2 (2+3x)) = 0

The product is zero if any of the terms is zero

(2+3x)^1/2 = 0 or 2 + 3^3/2 (2+3x)^3/2 = 0

First one of them gives the solution:
2+3x = 0 -> 3x = -2 -> x = -2/3

The solution checks out, too.

Second one:
3^3/2 (2+3x)^3/2 = 2

(2+3x)^3/2 = 2 / (3^3/2)

2+3x = 2^2/3 / 3

3x = 2+ 2^2/3 / 3

x = 2/3 + 2^2/3 / 9

This solution does not check out.

So the solution is

x = -2/3

Answer 4

31 1/2 x squared?
I don't know
4 times 2 = 8
8+3x = 11x
11x + 1/2 = 11 1/2 x
11 1/2 x + 3 = 14 1/2 x
14 1/2 x times 2 = 28 1/2 x
28 1/2 x + 3x = 31 1/2 x squared
31 1/2 x squared + 3/2 ?????????????????????
I don't know, I haven't done this in a long time Sorry

Answer 5

Well, you do have a problem here!

What you have stated is:

The SQUARE ROOT of {4(2+3x)} + the SQUARE ROOT of {3(2+3x)} CUBED i.e. to the power of 3

I could solve this for you but the limitations of available mathematical symbols in ANSWERS makes it very difficult to explain.

I shall be interested to see if someone to follow solves this for you.

So far nobody has!

Have a go using the information above.

Answer 6

Interesting. CurlyQ read the question as

The SQUARE ROOT of {4(2+3x)} + the SQUARE ROOT of {3(2+3x)} CUBED i.e. to the power of 3

but I took it to mean 4 times the square root of (2+3x) plus 3 times the square root of (2+3x) cubed.

But either way we are looking at the square root of a cubic equation. Are you just looking to simplify the expression or the find the zeros?

Answer 7

1?

Answer 8

i'm not really sure what you're looking for, but you can factor out (2+3x)^.5.

You would get (2+3x)^.5 * (4 + 3(2+3x)) which is (2+3x)^.5 * (10 + 9x) when simplified.

Answer 9

Having just completed a Phd in pure mathmatics I can assure you the answer is cacti.

Answer 10

[4*(2+3x)]^(1/2) + [3*(2+3x)]^(3/2)
Remember (a*b)^n = a^n*b^n
4^(1/2)*(2+3x)^(1/2) + 3^(3/2)*(2+3x)^(3/2)
Note 4^(1/2) = sqrt(4) = 2 and 3^(3/2) = (3^3)^(1/2)=3sqrt(3)
2*(2+3x)^(1/2) + 3sqrt(3)*(2+3x)^3/2
Factor out (2+3x)^(1/2)
(2+3x)^(1/2)[2+3sqrt(3)(2+3x)]
= (2+3x)^(1/2)[2 + 6sqrt(3) + 9xsqrt(3)]
or
sqrt(2+3x)*[2 + 6sqrt(3) + 9x*sqrt(3)]