Solve Equation Problem: 2a^(3/2) + (a^2-x^2)^(1/2)

[1/2"]

Hey there!
I have a few doubts regarding this worked out example in my book,
It goes like this…
Solve 2a ^ ^(3/2) +(a^²-x^²) ^ ^(1/2) {(a+x) ^ ^(1/2) +(a-x) ^ ^(1/2) }= a^ ^(2/3) +a{(a+x) ^{^(1/2)}+(a-x) ^^1/2}+(a^²-x^²) ^ ^(1/2)
Well now they say
Hence, removing from a^ ^{( 3/2)} both sides and transposing, we get
a^ ^(1/2) {a-(a^²-x^²) ^ ^(1/2) }= {(a+x) ^ ^(1/2) + (a-x ) ^ ^(1/2) }x { a-(a^ ² -x^²) ^ ^(1/2) }
whence a^ ^(1/2) = ( a+x) ^ ^(1/2) +(a-x) ^ ^(1/2) ;
squaring both sides a= 2a =2( a^²-x^²) ^ ^(1/2)
anyway it concludes as x= ± ( a√ 3)/2
But the problem is that I can’t understand how could 2a^^2/3 suddenly disappear!
Plz help me!

 

[tiny-tim]

Hey 1/2"!

(try using the X² tag just above the Reply box )

… But the problem is that I can’t understand how could 2a^2/3 suddenly disappear!

It's very difficult to read your equations, but I think the answer is that 2a²/3 hasn't disappeared …

a²/3 has disappeared from both sides, which is ok because you can always add or subtract the same amount from both sides (or indeed multiply or divide both sides by the same amount, or raise them to the same power)

 

[1/2"]

i am sorry for the mistakes !
I have corrected them . For futher mistake please let post it!

 

[tiny-tim]

Hi 1/2"!

(just got up :zzz: …)

First, you don't need ^ if you're using SUP (maybe in handwriting, where different levels aren't clear, but certainly not in typing), and you don't need brackets round (1/2) etc.

Quicker if I do that now …

Hey there!
I have a few doubts regarding this worked out example in my book,
It goes like this…
Solve 2a^3/2 +(a²-x²)^1/2 {(a+x)^1/2 +(a-x)^1/2 }= a^2/3 +a{(a+x)^1/2+(a-x)^1/2}+(a²-x²)^1/2
Well now they say
Hence, removing from a^2/3 both sides and transposing, we get
a^1/2 {a-(a²-x²)^1/2 }= {(a+x)^1/2 + (a-x )^1/2 }x { a-(a² -x²)^1/2 }
whence a^1/2 = ( a+x)^1/2 +(a-x)^1/2 ;
squaring both sides a= 2a =2( a²-x²)^1/2
anyway it concludes as x= ± ( a√ 3)/2
But the problem is that I can’t understand how could 2a^2/3 suddenly disappear!
Plz help me!

ok, now I think I can see what's happened …

either you or your book are misprinting "2/3" for "3/2" …

the a^1/2 {a that begins the second equation-line is the same as a^3/2, which is presumably what it should be throughout.

Does that sort it out? ​

 

[1/2"]

I'm sorry i don't get it.

 

[tiny-tim]

… Solve 2a ^ ^(3/2) +(a^²-x^²) ^ ^(1/2) {(a+x) ^ ^(1/2) +(a-x) ^ ^(1/2) }= a^ ^(2/3) +a{(a+x) ^{^(1/2)}+(a-x) ^^1/2}+(a^²-x^²) ^ ^(1/2)
Well now they say
Hence, removing from a^ ^{( 3/2)} both sides and transposing …
…
But the problem is that I can’t understand how could 2a^2/3 suddenly disappear!

I'm sorry i don't get it.

Well, the a^2/3 just after the = sign doesn't seem to match anything else in that equation, so I think it's a misprint for a^3/2