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Simply (x^(p)/x^(q))^(p+q)div((x^(p+q)...

Simply
`(x^(p)/x^(q))^(p+q)div((x^(p+q))/(x^(p-q)))^(p^(2)/(q))`

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int (dx)/((x-p)sqrt((x-p)(x-q)))

If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a common root, then it must be equal to a. (p^(prime)-p ^(prime) q)/(q-q^(prime)) b. (q-q ')/(p^(prime)-p) c. (p^(prime)-p)/(q-q^(prime)) d. (p q^(prime)-p^(prime) q)/(p-p^(prime))

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

Evaluate: int(dx)/((x-p)sqrt((x-p)(x-q)))

int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx is equal to (1)    -x^p/(x^(p+q)+1)+C     (2)    x^q/(x^(p+q)+1)+C     (3)    -x^q/(x^(p+q)+1)+C     (4)    x^p/(x^(p+q)+1)+C    

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CHHAYA PUBLICATION-LAWS OF INDICES-Short Answer Type Questions
  1. Simply (a^(p)/a^(q))^(p+q-r).(a^(q)/a^(r ))^(q+r-p).(a^(r )/a^(p))^...

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  2. Simply (x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-a)))^(1/(b-c))xx(x^(1/(c -a...

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  3. Simply (x^(p)/x^(q))^(p+q)div((x^(p+q))/(x^(p-q)))^(p^(2)/(q))

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  4. Prove (1/(1+x^(b-a)+x^(c-a)))+(1/(1+x^(a-b)+x^(c-b)))+(1/(1+x^(a-c)+...

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  5. Prove root(p+q)(x^(p^(2))/(x^(q^(2))))xxroot(q+r)(x^(q^(2))/(x^(r^(2...

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  6. Prove root(ln)((x^(l))/(x^(n)))xxroot(nm)((x^(n))/(x^(m)))xxroot(ml)...

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  7. If x=2^(2/3)+2^(1/3) show that x^(3)-6x=6

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  8. If a=2^(1/3)-2^(-1/3) show that 2a^(3)+6a-3=0

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  9. If x=2+2^(2/3)+2^(1/3) show that x^(3)-6x^(2)+6x-2=0

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  10. If x^(1/a)=y^(1/b)=z^(1/c ) and xyz =1 show that a+b+c=0

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  11. If a^(1/3)+b^(1/3)+c^(1/3)=0 show that (a+b+c)^(3)=27 abc

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  12. If x^(a)=y^(b)=(xy)^(c ) prove that ab=c(a+b)

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  13. If x^(a)=c^(b) and x^(c )=c^(a) show that a^(2)=bc

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  14. If x^(y)=y^(x) show that (x/y)^(x/y)=x^((x)/(y)-1) if further x=2y t...

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  15. If p^(a)=q^(b)=r^(c ) and pqr=1 show that ab+bc+ca=0

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  16. If 2^(x)=3^(y)=12^(z) show that xy=z(x+2y)

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  17. If (a-(1)/(a))^(2)=3 show that a^(6)+(1)/(a^(6))=110

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  18. If x^(3)=y^(4) prove that (x/y)^(4/3)+(y/x)^(3/4)=x^(1/3)+y^(-1/4)

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  19. If a^(x)=b,b^(y)=c,c^(z)=a show that xyz =1 (a,b,c positive num...

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  20. If (x^(n^3))^(n)=(x^(3^n))^(3) show that root(n+1)(n^(4))=3

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