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Mathematics
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Cookie
  • Member for 5 years
  • Last seen more than 2 years ago
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7
Given $a_1$, find an increasing sequence so that $a_1+\dots+a_k $ divides $ a_1^2+\dots+a_k^2$ for all $k$
Feb 16, 2023
3
Find the sum of $\frac{1}{\sqrt1+\sqrt3} + \frac{1}{\sqrt3+\sqrt5} + \frac{1}{\sqrt5+\sqrt7} + ... \frac{1}{\sqrt79+\sqrt81}$ [duplicate]
May 4, 2021
3
Solving the system $x^2+y^2+x+y=12$, $xy+x+y=-7$
Dec 26, 2021
3
Prove that there are no real numbers $a,b,c,d$ such that this system of equations holds.
Feb 26, 2022
3
Prove inequality for positive real numbers $x,y,z$
Oct 23, 2022
3
Prove $EB=EC$ and that $F,M,G,C$ are concyclic in the given figure
Dec 18, 2022
2
Let $x,y,z$ be positive real numbers such that $x^2+y^2+z^2=xyz$. Prove the following $xyz\geq27,xy+yz+zx\geq27,x+y+z\geq9$
Nov 17, 2021
2
For positive real numbers $a,b,c$ prove that $2+\frac{a^6+b^6+c^6}{3}\ge ab+ac+bc$
Nov 19, 2021
2
Solve this system of equations for real numbers
Dec 15, 2021
2
For positive real numbers $a,b,c$ prove that $2+\frac{a^6+b^6+c^6}{3}\ge ab+ac+bc$
Nov 19, 2021