(m²+n²)x² -2(mp+np)x + (b² + c²) =0

1.	(m²+n²)x² -2(mp+np)x + (b² + c²) =0
Answer» We have the following equation,{tex}(m^2+n^2)x^2-2(mp+nq)x+p^2+q^2=0{/tex}where, a =\xa0(m2 + n2), b =\xa0-2(mp + nq), and c = p2 + q2The given equation will have equal roots,if D = 0{tex}\\Rightarrow{/tex}\xa0{tex}b^2-4ac=0{/tex}{tex}\\Rightarrow{/tex}{tex}[-2(mp+nq)]^2-4(m^2+n^2)(p^2+q^2)=0{/tex}{tex}\\Rightarrow{/tex}{tex}4m^2p^2+4n^2q^2+8mnpq-4m^2p^2-4m^2q^2-4n^2q^2-4n^2p^2=0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}-4m^2q^2-4p^2n^2+8mnpq=0{/tex}\xa0{tex}\\Rightarrow{/tex}{tex}-4(m^2q^2+p^2n^2-2mnpq)=0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}m^2q^2+p^2n^2-2mnpq=0{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}(mq-pn)^2=0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}mq-pn=0{/tex}\xa0{tex}\\Rightarrow{/tex}{tex}mq=pn{/tex}

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