I think it’s a great equation to solve. The question should have stated x is a real number. So there are no domain restrictions for X. However m should always be positive coz it’s the square of x. In this case both 2 and the positive radical value providing two positive and two negative roots. The highest power of x is 8. Since x is real 4 roots are correct.
What I really value is the method. The substitution of n divides the expression in to 2 factors each having 4th power of the variable. Then the substitution of m split each of the above factors in to two quadratic factors. Good approach overall.
You reject the second option because you state that x must be a positive integer but then accept the first solution of root 2 - which is not an integer
I think it’s a great equation to solve. The question should have stated x is a real number. So there are no domain restrictions for X. However m should always be positive coz it’s the square of x. In this case both 2 and the positive radical value providing two positive and two negative roots. The highest power of x is 8. Since x is real 4 roots are correct.
What I really value is the method. The substitution of n divides the expression in to 2 factors each having 4th power of the variable. Then the substitution of m split each of the above factors in to two quadratic factors. Good approach overall.
Is √2 is an integer?
You reject the second option because you state that x must be a positive integer but then accept the first solution of root 2 - which is not an integer
If x is a positive integer then how sqrt 2 is an integer?
This is a very long, tedious and not logically concluded process.
Peux-tu expliquer pourquoi x devrait être un nombre entier ?
Reject t=-3, (1-√29) /2 outrightly
Then reject t=(1+√29) /2 as it will give x^4>7
If x>0 then how we will take -√2
Just substitute x^2=t
Also x^2=(1+√29) /2 value is rejected because in that case x^4>7
Solution by insight
Let x^2=t
t^2+rt(t+7)=7
2^2+rt9=7
t^2=2
x=rt2 or -rt2
m >0 , not x >0
U will get t=2, -3, (1+/-√29) /2
So only real solutiins are x=+/-√2
DIFFERENT APPROACH ( find the mistake challenge )
x^4 + √(x^2 + 7) = 7
x^2 = [7 - √(x^2 + 7)]^2
x^2 = 49 + x^2 + 7 -14√(x^2 + 7)
x squrt will cancel out and after furthur solving we will get,
√(x^2 + 7) = 56/14 = 4
x^2 = 16 -7 = 9
x = √9
x = ±3
Challenge -- find mistake
Il faut dire x = ±√9 (et non x = √9 , car √9 = 3 (jamais -3) !!
Sinon (±3)^4 + √((±3)^2 + 7) = 85 (et non 7) ^^
Your mistake is in the first step
X^2=[7-(√x^2+7)]^1/2
And instead of power 1/2 u have written 2.
Very long and tedious process.
Х^Х=7 ?
That's wrong.
Le résultat semble être bon, mais dans son raisonnement, il y a une (ou plusieurs) erreur(s)
Х= Корень из 2.
x=+_V2.