Question

if a+b =2√3 and ab=3 then a⁴+b⁴=? ​

Answer 1

Answer:

The answer is 18

Step-by-step explanation:

Given $a+b=2\sqrt 3$ and $ab=3$

Square both sides

 $\Rightarrow (a+b)^2=(2\sqrt 3)^2\\\Rightarrow a^2+b^2+2ab=4(3)\\\Rightarrow a^2+b^2+2(3)=12\\\Rightarrow a^2+b^2=12-6=6$

Again square both sides

 $\Rightarrow a^4+b^4+2a^2b^2=36\\\Rightarrow a^4+b^4+2(ab)^2=36\\\Rightarrow a^4+b^4+2(3)^2=36\\\Rightarrow a^4+b^4+18=36\\\Rightarrow a^4+b^4=36-18=18$