Easier solution method. Substitute x=y-10 into the given equation and rearrange to (y+1)^4+(y-1)^4-706=0. Pascal's Triangle 1 4 6 4 1 Combine terms: 2(y^4+6y^2+1)-706=0 or y^4+6y^2-352=0. Solve for y^2: y^2=(-6±38)/2=16 or -22. Finally, x=±4-10=-6 or -14 or x=-10±i√22
1:38 It is more easy to use Pascal triangles.
Easier solution method. Substitute x=y-10 into the given equation and rearrange to (y+1)^4+(y-1)^4-706=0. Pascal's Triangle 1 4 6 4 1
Combine terms: 2(y^4+6y^2+1)-706=0 or y^4+6y^2-352=0. Solve for y^2: y^2=(-6±38)/2=16 or -22.
Finally, x=±4-10=-6 or -14 or x=-10±i√22
That's a clever and efficient approach! Thanks for sharing 💯💕😎👏Thanks for sharing your insightful solution! 🔥🥰✅💕
X = -6 and -14 . The rest are complex numbers
Боже как все сложно
(x+9)⁴+(x+11)⁴=706
(x+10-1)⁴+(x+10+1)⁴=706
Let y=x+10
(y-1)⁴+(y+1)⁴=706
y⁴-4y³+6y²-4y+1
y⁴+4y³+6y²+4y+1
2y⁴+12y²+2=706
2y⁴+12y²-704=0
y⁴+6y²-352=0
(y²+22)(y²-16)=0
(y²+22)(y+4)(y-4)=0
y²+22=0
y²=-22
|y|=i√22
y=±i√22
x+10=±i√22
x=-10±i√22 ❤❤
y+4=0
y=-4
x+10=-4
x=-14 ❤
y-4=0
y=4
x+10=4
x=-6 ❤
let u=x+9 , u^4+(u+2)^4=706 , u^4+4u^3+12u^2+16u-345=0 , (u+5)(u^3-u^2+17u-69)=0 , (u-3)(u^2+2u+23)=0 , u^2+2u+23=0 ,
1 5 1 -3 u=(-2+/-V(4-92))/2 , u=(-2+/-i*V(88))/2 ,
-1 -5 2 -6 u= -1+i*V22 , -1-i*V22 , -5 , 3 ,
17 85 23 -69 x=u-9 , x= -10+i*V22 , -10-i*V22 , -14 , -6 ,
-69 -345 test x=-14 , --> 706 , x=-6 , --> 706 , x= -10+i*V22 , --> 706 , x= -10-i*V22 , --> 706 ,