Question

(z+3) (z-3) - (z-5) = 6

Answer 1

• We have to evaluate the above expression by using the given data.

             Given data:- $(z+3)(z-3)-(z-5)=6.$

             To find:- Value of above expression.

             Solution:-

              $=>(z+3)(z-3)-(z-5)=6 \\=>z(z-3)+3(z-3)-(z-5)=6\\=>z^{2}-3 z+3(z-3)-(z-5)=6 \\=>z^{2}-3 z+3 z-9-(z-5)=6\\=>z^{2}-3 z+3 z-9-(z-5)=6 \\=>z^{2}-9-(z-5)=6\\=>z^{2}-z-4-6=0 \\=>z^{2}-z-10=0\\=>z=\frac{1 \pm \sqrt{(-1)^{2}-4 \cdot 1(-10)}}{2 \cdot 1} \\=>z=\frac{1 \pm \sqrt{1-4 \cdot 1(-10)}}{2 \cdot 1}\\=>z=\frac{1 \pm \sqrt{1+40}}{2 \cdot 1} \\=>z=\frac{1 \pm \sqrt{41}}{2 \cdot 1}$

       Hence we will get$z=\frac{1+\sqrt{41}}{2}$ and$z=\frac{1-\sqrt{41}}{2}$.

Answer 2

To find : value of $z$

Given : $(z + 3 ) ( z -3 ) - (z -5 ) =6$

Solution :  

• Here, we will use the below following steps to find a solution using the transposition method:

1. We will Identify the variables and constants in the given equation.
2. Then we differentiate the equation as LHS and RHS.
3. We take constants at RHS leaving variable at LHS.  
4. Simplify the equation using arithmetic operation as required to find the value of $z$
5. Then the result will be the solution for the given linear equation. By using the transposition method. we get,

• $(z + 3 ) ( z -3 ) - (z -5 ) =6$  

        $z^{2}-3z +3z -9 -z + 5 =6\\z^{2} -9 -z+5 =6\\z^{2} -z -10 =0$

Hence , equation of above expression is $z^{2} -z -10 =0$ .