giá trị biểu thức P= (1+ căn 3)^2016.(3- căn 3)^2016 bằng 08/08/2021 Bởi Iris giá trị biểu thức P= (1+ căn 3)^2016.(3- căn 3)^2016 bằng
Đáp án: $A=12^{1008}$ Giải thích các bước giải: $A=(1+\sqrt{3})^{2016}.(3-\sqrt{3})^{2016}$ $\rightarrow A=(1+\sqrt{3})^{2016}.(\sqrt{3}(\sqrt{3}-1))^{2016}$ $\rightarrow A=(\sqrt{3}+1)^{2016}.(sqrt{3}-1)^{2016}.\sqrt{3}^{2016}$ $\rightarrow A=((\sqrt{3}+1)(\sqrt{3}-1))^{2016}.(3^\frac{1}{2})^{2016}$ $\rightarrow A=(\sqrt{3}^2-1)^{2016}.3^{\frac{1}{2}.2016}$ $\rightarrow A=(3-1)^{2016}.3^{1008}$ $\rightarrow A=2^{2016}.3^{1008}$ $\rightarrow A=(2^2)^{1008}.3^{1008}$ $\rightarrow A=4^{1008}.3^{1008}$ $\rightarrow A=(4.3)^{1008}$ $\rightarrow A=12^{1008}$ Bình luận
Đáp án:
$A=12^{1008}$
Giải thích các bước giải:
$A=(1+\sqrt{3})^{2016}.(3-\sqrt{3})^{2016}$
$\rightarrow A=(1+\sqrt{3})^{2016}.(\sqrt{3}(\sqrt{3}-1))^{2016}$
$\rightarrow A=(\sqrt{3}+1)^{2016}.(sqrt{3}-1)^{2016}.\sqrt{3}^{2016}$
$\rightarrow A=((\sqrt{3}+1)(\sqrt{3}-1))^{2016}.(3^\frac{1}{2})^{2016}$
$\rightarrow A=(\sqrt{3}^2-1)^{2016}.3^{\frac{1}{2}.2016}$
$\rightarrow A=(3-1)^{2016}.3^{1008}$
$\rightarrow A=2^{2016}.3^{1008}$
$\rightarrow A=(2^2)^{1008}.3^{1008}$
$\rightarrow A=4^{1008}.3^{1008}$
$\rightarrow A=(4.3)^{1008}$
$\rightarrow A=12^{1008}$