Rozłóż na czynniki pierwsze (kożystając z wzorów sktóconego mnożenia) Liceum ;) NAJ :D
x^4-25=
81x^4-1=
x^4-2=
x^4-25=(x^2-5)(x^2+5)
81x^4-1=(9x^2-1)(9x^2+1)
x⁴-25=(x²-5)(x²+5)=(x-√5)(x+√5)(x²+5)
81x⁴-1=(9x²-1)(9x²+1)=(3x-1)(3x+1)(9x²+1)
x⁴-2=(x²-√2)(x²+√2)=(x-⁴√2)(x+⁴√2)(x²+√2)
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x^4-25=(x^2-5)(x^2+5)
81x^4-1=(9x^2-1)(9x^2+1)
x^4-2=![(x^{2}-\sqrt{2})(x^{2}+\sqrt{2})=(x- \sqrt[4]{2})(x+ \sqrt[4]{2})(x^{2}+\sqrt{2}) (x^{2}-\sqrt{2})(x^{2}+\sqrt{2})=(x- \sqrt[4]{2})(x+ \sqrt[4]{2})(x^{2}+\sqrt{2})](https://tex.z-dn.net/?f=%28x%5E%7B2%7D-%5Csqrt%7B2%7D%29%28x%5E%7B2%7D%2B%5Csqrt%7B2%7D%29%3D%28x-+%5Csqrt%5B4%5D%7B2%7D%29%28x%2B+%5Csqrt%5B4%5D%7B2%7D%29%28x%5E%7B2%7D%2B%5Csqrt%7B2%7D%29)
x⁴-25=(x²-5)(x²+5)=(x-√5)(x+√5)(x²+5)
81x⁴-1=(9x²-1)(9x²+1)=(3x-1)(3x+1)(9x²+1)
x⁴-2=(x²-√2)(x²+√2)=(x-⁴√2)(x+⁴√2)(x²+√2)