Class-eight_math_img

m+\displaystyle \frac{1}{m}=2 হলে, প্রামান কর যে, m\displaystyle ^{4}+\displaystyle \frac{1}{m^{4}}=2

দেওয়া আছে,
m+\displaystyle \frac{1}{m}=2
বামপক্ষ=m\displaystyle ^{4}+\displaystyle \frac{1}{m^{4}}
= (m\displaystyle ^{2})\displaystyle ^{2}+\displaystyle \left(\frac{1}{m^{2}}\right)^{2}
=\displaystyle ( m^{2}+\displaystyle \frac{1}{m^{2}})\displaystyle ^{2}– 2.\displaystyle m^{2}.\displaystyle \frac{1}{m^{2}}
=\displaystyle \left{( m)^{2} +\left(\frac{1}{m}\right)^{2}\right}^{2}– 2
={(\displaystyle m+\frac{1}{m})\displaystyle ^{2} -2.m.\displaystyle \frac{1}{m}}\displaystyle ^{2} -2
=\displaystyle {( 2)^{2}-2}\displaystyle ^{2}-2
=(4-2)\displaystyle ^{2}-2
=(2)\displaystyle ^{2}-2
=4-2
=2
=ডানপক্ষ

m\displaystyle ^{4}+\displaystyle \frac{1}{m^{4}}=2 (প্রামানিত)

অথবা….

Class-eight_math_img
দেওয়া আছে,

m+\displaystyle \frac{1}{m}=2
\displaystyle \frac{m^{2} +1}{m}=2
\displaystyle m^{2} +1=2m
\displaystyle m^{2}-2m+1=0
\displaystyle m^{2} -2.m.1+1^{2} =0
\displaystyle ( m-1)^{2}=0 (উভয় পক্ষ বর্গ করে পাই)
\displaystyle m-1=0
m=1

এখন,,,
\displaystyle m^{4} +\frac{1}{m^{4}}
=1\displaystyle ^{4} +\frac{1}{1^{4}}
=1+1
=2 ((প্রামানিত)

Post Author: showrob

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