Giải bài 5 trang 53

Đề bài

Chứng minh:

a) $\left(\sqrt{2025}-\sqrt{2024}\right)\left(\sqrt{2025}+\sqrt{2024}\right)=1$

b) $\left(\sqrt[3]{33}-1\right)\left[{\left(\sqrt[3]{33}\right)}^2+\sqrt[3]{33}+1\right]=2$

c) ${\left(\sqrt{3}-2\right)}^2{\left(\sqrt{3}+2\right)}^2=1$

Lời giải chi tiết

a) $VT=\left(\sqrt{2025}-\sqrt{2024}\right)\left(\sqrt{2025}+\sqrt{2024}\right)$

$\begin{array}{c}={\left(\sqrt{2025}\right)}^2-{\left(\sqrt{2024}\right)}^2\\ =2025-2024\end{array}$

$=1=VP.$(đpcm)

b) $VT=\left(\sqrt[3]{33}-1\right)\left[{\left(\sqrt[3]{33}\right)}^2+\sqrt[3]{33}+1\right]$

$={\left(\sqrt[3]{33}\right)}^3-1$

$=3-1=2=VP$ (đpcm).

c) $VT={\left(\sqrt{3}-2\right)}^2{\left(\sqrt{3}+2\right)}^2$

$={\left[\left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right)\right]}^2={\left[{\left(\sqrt{3}\right)}^2-4\right]}^2$

$={\left(3-4\right)}^2={\left(-1\right)}^2=1=VP$ (đpcm).