Question

x-1/x=4 হলে, x²+x+1/x²-1/x= ?​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{x-\dfrac{1}{x}=4\,\,\,\,\,\,\,\,\,\,...(1)}$

$\tt{\implies\,\left(x-\dfrac{1}{x}\right)^2=\left(4\right)^2}$

$\tt{\implies\,{x}^{2}+\dfrac{1}{{x}^{2}}-2\cdot\,x\cdot\dfrac{1}{x}=16}$

$\tt{\implies\,{x}^{2}+\dfrac{1}{{x}^{2}}-2=16}$

$\tt{\implies\,{x}^{2}+\dfrac{1}{{x}^{2}}=16+2}$

$\tt{\implies\,{x}^{2}+\dfrac{1}{{x}^{2}}=18\,\,\,\,\,\,\,\,\,...(1)}$

Now,

$\rm{{x}^{2}+x+\dfrac{1}{{x}^{2}}-\dfrac{1}{x}}$

$\rm{={x}^{2}+\dfrac{1}{{x}^{2}}+x-\dfrac{1}{x}}$

$\rm{=\left({x}^{2}+\dfrac{1}{{x}^{2}}\right)+\left(x-\dfrac{1}{x}\right)}$

From (1) and (2),

$\rm{=18+4}$

$\rm{=22}$