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52 Show that a(b - c)x^2 + b(c - a)xy +...

52 Show that `a(b - c)x^2` +` b(c - a)xy` + `c(a - b)y^2` will be a perfect square if a, b, c are in H.P

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If the expression x^2+2(a+b+c)x+3(bc+ca+ab) is a perfect square then

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  2. If (a1x^2 +bx+c1)y+(a2x^2+b2x+c1)=0 find condition that x is a ration...

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  3. 52 Show that a(b - c)x^2 + b(c - a)xy + c(a - b)y^2 will be a perfect...

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  4. For what value of k, (x + y + z)^2 + k(x^2 +y^2 + z^2) can be resolve...

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  5. If (x-1)^(2) is a factor of ax^(3) +bx^(2) +c then roots of the equa...

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  6. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

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  7. If |x|+|x-1|=3 then x= .

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  8. The solution-set of the equation log5log2(sqrt(4x+2)+2sqrt2)=0 is .

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  9. Fill in the blanks If x<0,y<0,x+y+(x//y)=(1//2)a n d(x+y)(x//y)=-(1//2...

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  10. The number of real solutions of the equation |x^2|-3|x|+2=0 is .

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  11. If x-=2+^(2//3)"then the value"(x^(3)-6x^(2)+6x)is

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  12. The AM of the roots of x^2-12x+3=0 is .

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  13. The GM of the roots of x^3-6x^2+11x-6=0 is .

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  14. The quadratic equation whose roots are twice the roots of x^2-3x+3=0 i...

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  15. The quadratic equation whose roots are 2 more than the roots of ax^2+b...

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  16. If alpha,beta are roots of ax^2+2bx+c=0 then sqrt(alpha/beta)+sqrt(bet...

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  17. if 2 = I sqrt3 be a root of the equation x^(2) + px + q =0, where p ...

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  18. The value of sqrt(2+sqrt(2+sqrt(2+......oo is .

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  19. If the roots of x(3-x^2)+2x^2=0 are alpha,beta,gamma then the value of...

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  20. If the roots of 4-3x+5x^2+x^3=0 are alpha,beta,gamma then the value of...

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