Changes
From Karnataka Open Educational Resources
1,082 bytes removed
, 11:33, 14 August 2014
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| | <math>p^3+q^3</math> | | <math>p^3+q^3</math> |
| | [[solution]] | | [[solution]] |
| − | '''Pre requisites''':
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| − | #Standard form of quadratic equation
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| − | #Formula to find the sum & product of quadratic equation
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| − | #Knowledge of using appropriate identity
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| − | '''Interpretation of the Problem''':
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| − | #Compare the equation with standard form and identify the values of a,b,c
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| − | #To find the sum formformof the roots of the quadratic equation using the formula
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| − | #To find the product of the roots of the equation
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| − | # Using the identity & rewriting <math>p^3+q^3</math> as <math>(p+q)^3-3pq(p+q)</math>
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| − | #Substitute the values of m+n & mn in <math>(p+q)^3-3pq(p+q)</math>
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| − | #Simplification
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| − | '''Concepts''':
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| − | #Formula to find the sum and product of the roots of the quadratic equation
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| − | #Identity <math>(a+b)^3=a^3+b^3+3ab(a+b)</math>
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| − | '''Algorithm''': <br>
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| − | Consider the equation <math>2a^2-4a+1=0</math><br>
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| − | Here a=2,b=-4 & c=1<br>
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| − | If p & q are the roots of the quadratic equation then<br>
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| − | <math>p+q={\frac{-b}{a}}={\frac{-(-4)}{2}=2}</math><br>
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| − | <math>pq={\frac{c}{a}}={\frac{1}{2}}</math><br>
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| − | Therefore,<br>
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| − | <math>p^3+q^3=(p+q)^3-3pq(p+q)</math><br> =<math>(2)^3-3[{\frac{1}{2}}](2)</math><br>
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| − | =8-3<br>=5
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| | | | |
| | =Ex.no.9.11 /problem no.9= | | =Ex.no.9.11 /problem no.9= |
