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  • How to solve this problem- - Integral Calculus - JEE Main-7

What is the perfect square for of -x^{2}+2kx+4k

  • Option 1)

    (x+k)^{2}+4k-k^{2}

  • Option 2)

    -(x+k)^{2}+k^{2}-4k

  • Option 3)

    -(x+k)^{2}+k^{2}+4k

  • Option 4)

    -(x+k)^{2}-k^{2}+4k

 

Answers (1)

best_answer

AS we have learned

Integration by perfect square method -

ax^{2}+bx+c=a\left [ x^{2}+\frac{bx}{a}+\frac{c}{a} \right ]=a\left [ \left ( x+\frac{b}{2a} \right )^{2}+\frac{c}{a}-\frac{b^{2}}{4a^{2}} \right ]

- wherein

Make the coefficient of x^{2} +ve one . 

 

-x^{2}+2kx+4k

=-(x^{2}+2kx)+4k

=-(x^{2}+2kx+ k) ^{2} +4k+k^{2}

=-(x+ k) ^{2} +4k+k^{2} 

 

 

 

 


Option 1)

(x+k)^{2}+4k-k^{2}

This is incorrect

Option 2)

-(x+k)^{2}+k^{2}-4k

This is incorrect

Option 3)

-(x+k)^{2}+k^{2}+4k

This is correct

Option 4)

-(x+k)^{2}-k^{2}+4k

This is incorrect

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gaurav

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