Question

calculati: a)(x+1)(x-1)(xla a2 +1); b)(a+b)(a-b)(a la a2+b la a2); c)(a la a2+4)(a+2)(a-2); d)(radical din 2 +x)(radical din 2-x)(2+x la a 2); e)(a-1)(a+1)(a la a2+1)(a la a4+1); f)(a-radical din 2)(a +radical din 2)(a la a2+2)(a la a4+4); g)(radical din radical din2 +1)(radical din radical din2-1)(radical din radical din 3 +radical din 2)(radical din radical din 3-radical sin 2)

Answer 1

a) (x+1)(x-1)(x^{2} +1)=(x^{2} -1)(x^{2} +1)=x^{4}-1=>x=1
b) (a+b)(a-b)(a^{2}+b^{2})=(a^{2}-b^{2})(a^{2}+b^{2})=a^{4}-b^{4}=>a=b 
c) (a^{2}+4)(a+2)(a-2)=(a^{2}+4)(a^{2}-4)=a^{4}-16=>a=2
d) (\sqrt{2}+x)(\sqrt{2}-x)(2+x^{2})=(2-x^{2})(2+x^{2})=4-x^{4}=>x=\sqrt{2}
e) (a-1)(a+1)(a^{2}+1)(a^{4}+1)=(a^{2}-1)(a^{2}+1)(a^{4}+1)=(a^{4}-1)(a^{4}+1)=a^{8}-1=>a=1
f) (a-\sqrt{2})(a-\sqrt{2})(a^{2}+2)(a^{4}+4)=(a^{2}-2)(a^{2}+2)(a^{4}+4)=(a^{4}-4)(a^{4}+4)=a^{8}-16=a^{8}=16=>a^{8}=\sqrt{2}^{8}=>a=\sqrt{2}
g) (\sqrt{\sqrt{2}}+1)(\sqrt{\sqrt{2}}-1)(\sqrt{\sqrt{3}}+\sqrt{2})(\sqrt{\sqrt{2}}-\sqrt{2})=(\sqrt{2}-1)(\sqrt{3}-2)=\sqrt{6}-2\sqrt{2}-\sqrt{3}+2

x^{2} = x la a doua.
\sqrt{x} = radical din x la a doua
\sqrt{ \sqrt{x} } = radical din radical din x