\(\frac{2^3.5.7.5^2.7^3}{\left(2.5.7^2\right)^2}=\frac{2^3.5^3.7^4}{2^2.5^2.7^4}=2.5=10\)

x⁴+1-2x²

=x⁴+2x³+x²-2x³-4x²-2x+x²+2x+1

=x²(x²+2x+1)-2x(x²+2x+1)+1(x²+2x+1)

=(x²-2x+1)(x²+2x+1)

=(x-1)²(x+1)²

\(\left(a^2+4b^2\right)^2-16a^2b^2=\left(a^2+4b^2\right)-\left(4ab\right)^2=\left(a^2-4ab+4b^2\right)\left(a^2+4ab+4b^2\right)=\left(a-2b\right)^2\left(a+2b\right)^2\)

Gọi d = (5n + 3 ; 3n + 2) (d thuộc N) 
=> (5n + 3) chia hết cho d và (3n + 2) chia hết cho d 
=> 5.(3n + 2) - 3.(5n + 3) chia hết cho d 
=> 1 chia hết cho d 
=> d = 1 (vì d thuộc N) 
=> ƯCLN(5n + 3 ; 3n + 2) = 1 
=> Phân số 5n+3/3n+2 tối giản với mọi n thuộc N

\(\sqrt{3-2\sqrt{2}}=\sqrt{2-2\sqrt{2}+1}=\sqrt{\left(\sqrt{2}\right)^2-2\sqrt{2}+1^2}=\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{2}-1\left(vì:\sqrt{2}>\sqrt{1}=1\right)\)

\(\sqrt{7+4\sqrt{3}}=\sqrt{4+4\sqrt{3}+3}=\sqrt{\left(2\right)^2+2.2\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(2+\sqrt{3}\right)^2}=2+\sqrt{3}\left(2+\sqrt{3}>0\right)\)

\(\sqrt{28-10\sqrt{3}}=\sqrt{25-10\sqrt{3}+3}=\sqrt{5^2-2.5\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(5-\sqrt{3}\right)^2}=5-\sqrt{3}\left(vì:5=\sqrt{25}>\sqrt{3}\right)\)

( 2x + 1 ) ³  = 125

( 2x + 1 )³ = 5³

2x + 1 = 5

2x       = 5 - 1 = 4

x       = 4 : 2

x = 2

vậy x = 2