Prove that if \(a\ge3\), \(b\ge3\), \(a^2+b^2\ge25\) then \(a+b\ge7\)

Given abcd = 1. Prove that: \(a^2+b^2+c^2+d^2+ab+cd\ge6\)

Given f(x) satisfys: \(x\cdot f\left(x+2018\right)=\left(x+2016\right)\cdot f\left(x\right)\). Prove that f(x) = 0 with x = 0 and -2018.

Given \(\Delta ABC\), bisectris AD, point E and F in AD so that \(\widehat{ABE}=\widehat{CBF}\). Prove that: \(\widehat{ACE}=\widehat{BCF}\)

Find \(n\in N\) so that \(n^5-n+2\) is a square number

Find \(n\in N\) so that \(\dfrac{n^2+3n}{4}\) is a prime number

Find \(n\in N\) so that \(8n^2+10n+3\) is a prime number

Find \(n\in N\) so that \(12n^2-5n-25\) is a prime number.

Prove that the product of four consecutive integers is not a square number.

Prove that the product of three consecutive integers is not a square number.

Is \(B=144...44\) (99 4s) a square number?

Given a,b,c,d satisfys \(ab=cd\). Prove that: \(a^5+b^5+c^5+d^5\) isn't a prime number.

Compare: \(8\sqrt{3}\) with \(5\sqrt{7}\)

Find x,y,z satisfys: \(\dfrac{x}{8}=\dfrac{y}{3}=\dfrac{z}{10}\) and xy + yz + zx = 1206

Prove that there are no \(x,y\in Z\) satisfys: \(4x^2-7y^2=6\)

Prove that there are no \(x,y\in Z\) satisfys: \(9x^2-8y^2=15\)

Prove that: the sum of 9 numbers equals 10 always have a number larger than 1.

Given \(P\left(x\right)+3P\left(2\right)=5x^2\left(\forall x\right)\). Calculate P(3)

Given \(f\left(x\right)=ax^3+bx^2+cx+d\) with \(a\in Z+\). Known that \(f\left(5\right)-f\left(4\right)=2012\). Prove that \(f\left(7\right)-f\left(2\right)\) is not a prime number.

Alexa has x apples and 4y oranges. If she has the same number of apples and oranges, what is the ratio of x to y? Express your answer as a common fraction.