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Line 165: − '''Pre requisites''': − #Standard form of quadratic equation − #Formula to find the sum & product of quadratic equation − #Knowledge of using appropriate identity − '''Interpretation of the Problem''': − #Compare the equation with standard form and identify the values of a,b,c − #To find the sum formformof the roots of the quadratic equation using the formula − #To find the product of the roots of the equation − # Using the identity & rewriting <math>p^3+q^3</math> as <math>(p+q)^3-3pq(p+q)</math> − #Substitute the values of m+n & mn in <math>(p+q)^3-3pq(p+q)</math> − #Simplification − '''Concepts''': − #Formula to find the sum and product of the roots of the quadratic equation − #Identity <math>(a+b)^3=a^3+b^3+3ab(a+b)</math> − '''Algorithm''': <br> − Consider the equation <math>2a^2-4a+1=0</math><br> − Here a=2,b=-4 & c=1<br> − If p & q are the roots of the quadratic equation then<br> − <math>p+q={\frac{-b}{a}}={\frac{-(-4)}{2}=2}</math><br> − <math>pq={\frac{c}{a}}={\frac{1}{2}}</math><br> − Therefore,<br> − <math>p^3+q^3=(p+q)^3-3pq(p+q)</math><br> =<math>(2)^3-3[{\frac{1}{2}}](2)</math><br> − =8-3<br>=5
→Hints for difficult problems
<math>p^3+q^3</math>
<math>p^3+q^3</math>
[[solution]]
[[solution]]
=Ex.no.9.11 /problem no.9=
=Ex.no.9.11 /problem no.9=