Question

The root of the equation \[2y = 5(3 + y)\] is

Answer 1

Hint: A root of an equation in one variable is a value of the variable that satisfies the equation. Every equation in one variable with constants as coefficients and positive integers as exponents, has as many roots as the exponents of the highest power. In other words, the number of roots is the same as the degree of the equation.
For example: - A fourth degree equation has four roots, cubic has 3 roots.
For example: - \[x - 3 = 2\] is an equation in one variable. Both \[(x - 3)\]and \[2\] are functions. The letter is a constant function.
Roots are also called x-intercepts or zeros. The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, \[a{x^2}\; + {\text{ }}bx{\text{ }} + {\text{ }}c{\text{ }} = {\text{ }}0\].

Complete step by-step solution-:
Given equation is \[2y = 5(3 + y)...........(i)\]
 On multiplying 5 with the term present in the bracket we get
\[ \Rightarrow 2y = 15 + 5y\]
Now on transposing \[5y\] to the L.H.S we get
\[ \Rightarrow 2y - 5y = 15\]
\[ \Rightarrow - 3y = 15\]
\[ \Rightarrow y = - \dfrac{{15}}{3}\] {Transposing -3 to R.H.S denominator}
\[ \Rightarrow y = - 5\]
Required Root of \[E{q^n}\] is \[ - 5\].

Note: Now to check whether the solution is correct or wrong we have a trick to find it.
 So here \[y = - 5\] tells us that if \[y = - 5\] if we put the ‘y’ value in equation (i) if it satisfies the given \[e{q^n}\] then our solution is correct or else its wrong.
Now on applying the above method and simplifying we get
\[ \Rightarrow 2x - 5 = 5(3 + ( - 5))\]
\[ \Rightarrow - 10 = 5(3 - 5)\] {Firstly, solve Bracket}
Here the equation is satisfied hence our solution is correct.