equations involving radicals

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har

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I am using * in place of the radical sign because I dont have that symbol availbe
*5t+4*-2*t*=1
I added 2*t*to both sides in order to get the radicals on opposite sides
I then got
*5t+4*=2*t*+1
I then squared both sides to eliminate the ioslated radicals
(*5t+4*)^2=(2*t*+1)^2
I am lost here
I know that *5t+4* squared is
5t+4 but Im not sure how to square other side
I think it would be 4t +1 but I think I am wrong
 
How about just typing sqrt(5t+4)-sqrt(2t)?.

I assume you mean:

\(\displaystyle \sqrt{5t+4}-\sqrt{2t}=1\)

If so, it has no solutions.

If not, please correct me.
 
no what i meant is to keep the 2 before the radical of t
 
Okey -doke then.

\(\displaystyle \sqrt{5t+4}-2\sqrt{t}=1\)

\(\displaystyle \sqrt{5t+4}=1+2\sqrt{t}\)

Square both sides:

\(\displaystyle 5t+4=(1+2\sqrt{t})^{2}\)

\(\displaystyle 5t+4=1+4\sqrt{t}+4t\)

\(\displaystyle t+3=4\sqrt{t}\)

Square both sides:

\(\displaystyle t^{2}+6t+9=16t\)

\(\displaystyle t^{2}-10t+9=0\)

solve the quadratic. It has two solutions and can be easily factored. Be sure to check both solutions. One may not be a viable solution.
 
again I am using the * sign in place of the radical sign
when you do the square of (1+2*t*)^2 how does it produce
1+4*t*+4t
It looks like it would be 1+4t^2
1 squared is still 1
2 squared is 4
and t squared is t^2
 
har said:
again I am using the * sign in place of the radical sign
when you do the square of (1+2*t*)^2 how does it produce


The same way (a + b)[sup:10wvqmm4]2[/sup:10wvqmm4] produces a[sup:10wvqmm4]2[/sup:10wvqmm4] + b[sup:10wvqmm4]2[/sup:10wvqmm4]+ 2*a*b

(a+b)[sup:10wvqmm4]2[/sup:10wvqmm4] = (a + b) * (a + b) = a * (a + b) + b * (a + b) = a[sup:10wvqmm4]2[/sup:10wvqmm4] + a*b + a*b + b[sup:10wvqmm4]2[/sup:10wvqmm4] = a[sup:10wvqmm4]2[/sup:10wvqmm4] + 2*a*b + b[sup:10wvqmm4]2[/sup:10wvqmm4]

(1 + ?t)[sup:10wvqmm4]2[/sup:10wvqmm4] = (1 + ?t) * (1 + ?t)

like the example use FOIL to multiply the expressions and add "like" terms....

1+4*t*+4t
It looks like it would be 1+4t^2
1 squared is still 1
2 squared is 4
and t squared is t^2
Click to expand...
 
Ok so i understand that side now, but how did 5t+4 turn into t+3
I see that you subtracted the I from both sides turning the 4 into 3, but why did the 5 leave
 
har said:
Ok so i understand that side now, but how did 5t+4 turn into t+3
I see that you subtracted the I from both sides turning the 4 into 3, but why did the 5 leave
Click to expand...

In stead of looking at the solution - you should work with pencil and paper and write down - it would be obvious.

5t - 4t = 1t = t
 
Please stop it with those asterisks :roll: . Use sqrt() as I mentioned before. Wouldn't that make a bit more sense?.
 
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