0
votes
1answer
65 views

Is there any simple analytic method for solving $\sqrt{x}+y=7$ and $x+\sqrt{y}=11$ simultaneously. [duplicate]

I am thinking of a nice and simple analytic method to solve the following equations simultaneously: $$\sqrt x+y=7;\\x+\sqrt y=11.$$ To my suprise I can't. But, I solve the system numerically using ...
0
votes
1answer
21 views

Help inverting a non-linear system of equations

I have a set of two equations like this $$ \gamma_3=\left(\frac{1}{\sqrt{1+2c_3^2+6c_4^2}}\right)^3 \left( \alpha_1\,c_3^3 + \alpha_2\,c_3c_4^2 + \alpha_3\,c_3c_4 + \alpha_4\,c_4\right)\\ ...
0
votes
3answers
32 views

simultaneous equations with irrational variables

Solve the simultaneous equations $a\sqrt a+b\sqrt b=183$ and $a\sqrt b+b\sqrt a=182$ I made an attempt in vain to equate the coefficients and eliminate
1
vote
0answers
78 views

Geometry aspect of a extreme value problem

In a plain with orthogonal coordinate $XOY$, set point $A(a,a)$, and $P$ is a point in function $y=\frac{1}{x}$,where $x>0$. If the distance between $P$ and $A$ is $2\sqrt{2}$.Find all $a$ ...
1
vote
1answer
78 views

Solve …

This is what I did Can anyone tell me what's wrong me or the question?
1
vote
1answer
82 views

Roots of unity and a system of equations by Ramanujan

Is it immediately apparent that the solution to the system of equations, $$\begin{aligned} x_1^2 &= x_2+2\\ x_2^2 &= x_3+2\\ x_3^2 &= x_4+2\\ &\vdots\\ x_n^2 &= x_1+2\\ ...
4
votes
1answer
93 views

Ramanujan's curious cubic identities

Given the cubic, $$z^3-ez^2+fz-1=0$$ Let $z_1,z_2,z_3$ be the three roots. Define, $$x_n = z_1^{1/n}+ z_2^{1/n}+ z_3^{1/n}$$ $$y_n = (z_1z_2)^{1/n}+ (z_1z_3)^{1/n}+(z_2z_3)^{1/n}$$ Ramanujan found ...
3
votes
2answers
86 views

Finding the values of $a$ and $b$ [duplicate]

We are given two equations: $$ \left\{ \begin{array}{c} \sqrt{a}+b=11 \\ a+\sqrt{b}=7 \\ \end{array} \right. $$ How to find the value of $a$ and $b$ by solving the equation? All I could do was use ...
2
votes
2answers
576 views

system of equations $\sqrt{x}+y = 11$ and $x+\sqrt{y} = 7$. [duplicate]

If $x,y\in \mathbb{R}$ and $\sqrt{x}+y = 11\;$ and $x+\sqrt{y} = 7$. Then $(x,y) = $ $\underline{\bf{My\;\; Try::}}$ Let $x=a^2$ and $y=b^2$, Then equation is $a+b^2 = 11$ and $a^2+b = 7$. ...
0
votes
1answer
76 views

How to solve this system of equation?

I need to solve the following system of $(x,y)$: \begin{cases} 3y^3+3x\sqrt{1-x}=5\sqrt{1-x}-2y\\ x^2-y^2\sqrt{1-x}=\sqrt{2y+5}-\sqrt{1-x} \end{cases}
3
votes
3answers
297 views

Solutions to $\sqrt{x}+y=6,x^2+y^2=90$

$$\begin{gather} \sqrt{x}+y=6 \tag{1} \\ x^2 + y^2 = 90 \tag{2} \end{gather}$$ WE have to solve for $x$ and $y$(Note that 9 is an obvious value of x) My friend asked me this question earlier today, ...
4
votes
3answers
81 views

Is this solution correct?

$$\sqrt{x}+y=4\tag{A}$$ $$x+\sqrt{y}=6\tag{B}$$ Subtracting A from B, we have $$x-y -\sqrt{x}+\sqrt{y}=2$$ $$(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y}-1)=2$$ ...
6
votes
2answers
177 views

System of two Equations

A friend of Mine gave me a system of two equations and asked me to solve them $\rightarrow$ $$\sqrt{x}+y=11~~ ...1$$ $$\sqrt{y}+x=7~~ ...2$$ I tried to solve them manually and got this horrendously ...
3
votes
4answers
1k views

Steps to solve this system of equations: $\sqrt{x}+y=7$, $\sqrt{y}+x=11$

I want to solve this system of equations, I have been out of Maths for a long!! $$\sqrt{x}+y=7$$ $$\sqrt{y}+x=11$$ Just wondering easiest step to find values for $x$ and $y$ from the above ...