\(a>b>0\Rightarrow a+b>0\)

\(\left(a+b\right)^2=\left(a-b\right)^2+4ab=7^2+4.60=289\Rightarrow a+b=17\)

\(\Rightarrow a^2-b^2=\left(a-b\right)\left(a+b\right)=7.17=119\)

\(a^2+b^2=\left(a-b\right)^2+2ab=7^2+2.60=169\)

\(\Rightarrow a^4+b^4=\left(a^2+b^2\right)^2-2\left(ab\right)^2=169^2-2.60^2=21361\)

\(a^2-b^2=\left(a-b\right)\left(a+b\right)\)

\(=7\cdot\sqrt{\left(a-b\right)^2+4ab}\)

\(=7\cdot\sqrt{7^2+4\cdot60}=119\)

Ta có a - b = 1

=> (a - b)² = 1

<=> a² + b² - 2ab = 1

<=> a² + b² = 25

=> (a² + b²)² = 625

<=> a⁴ + b⁴ + 2(ab)² = 625

<=> a⁴ + b⁴ = 625 - 2.12² = 337

\(a,a^2+b^2=\left(a+b\right)^2-2ab=9^2-2\cdot20=41\\ b,a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2=41^2-2\left(ab\right)^2\\ =1681-2\cdot400=881\\ c,\left(a-b\right)^2=a^2+b^2-2ab=41-2\cdot20=1\\ \Rightarrow a-b=1\\ \Rightarrow C=a^2-b^2=\left(a-b\right)\left(a+b\right)=9\cdot1=9\)

\(a+b+c=0\Rightarrow\left(a+b+c\right)^2=0\)

\(\Rightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)

\(\Rightarrow ab+bc+ca=-5\)

\(\Rightarrow\left(ab+bc+ca\right)^2=25\)

\(\Rightarrow\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2+2abc\left(a+b+c\right)=25\)

\(\Rightarrow\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2=25\)

\(\Rightarrow a^4+b^4+c^4=\left(a^2+b^2+c^2\right)^2-2\left[\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2\right]\)

\(=10^2-2.25=50\)

Ta có: a+b+c=0 ⇒(a+b+c)²=0

Hay a²+b²+c²+2ab+2bc+2ca=0

1+2(ac+bc+ca)=0

ab+bc+ca=\(\dfrac{-1}{2}\)

\(\left(a^2+b^2+c^2\right)^2=a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=100\left(1\right)\)

\(\left(ab+bc+ca\right)^2=a^2b^2+b^2c^2+c^2a^2+b^2ac+c^2ab+a^bc=a^2b^2+b^2c^2+c^2+a^2+2abc\left(a+b+c\right)=a^2b^2+b^2c^2+c^2a^2=25\)

hay \(2\left(a^2b^2+b^2c^2+c^2a^2\right)=50\left(2\right)\)

Từ (1) và (2) ⇒a⁴+b⁴+c⁴=50

giúp mình vs mình đang cần gấp ạ

\(a^2+b^2=\left(a+b\right)^2-2ab=7^2-24=25\)

\(\left(a-b\right)^2=\left(a+b\right)^2-4ab=7^2-4.12=1\)

\(\Rightarrow a-b=-1\)

\(\Rightarrow A=\left(-1\right)^5=?\)

\(B=\left(a^2+b^2\right)^2-2\left(ab\right)^2=25^2-2.12^2=?\)