(m²+n²)x² -2(mp+np)x + (b² + c²) …
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Sia ? 6 years, 6 months ago
We have the following equation,
{tex}(m^2+n^2)x^2-2(mp+nq)x+p^2+q^2=0{/tex}
where, a = (m2 + n2), b = -2(mp + nq), and c = p2 + q2
The given equation will have equal roots,if D = 0
{tex}\Rightarrow{/tex} {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} {tex}-4m^2q^2-4p^2n^2+8mnpq=0{/tex}
{tex}\Rightarrow{/tex}{tex}-4(m^2q^2+p^2n^2-2mnpq)=0{/tex}
{tex}\Rightarrow{/tex} {tex}m^2q^2+p^2n^2-2mnpq=0{/tex}
{tex}\Rightarrow{/tex} {tex}(mq-pn)^2=0{/tex}
{tex}\Rightarrow{/tex} {tex}mq-pn=0{/tex}
{tex}\Rightarrow{/tex}{tex}mq=pn{/tex}
0Thank You