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If x, a, b, c are real and (x-a+b)^(2)+(...

If x, a, b, c are real and `(x-a+b)^(2)+(x-b+c)^(2)=0`, then a, b, c are in

A

H.P.

B

G.P.

C

A.P.

D

none of these

Text Solution

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The correct Answer is:
To solve the equation \((x - a + b)^2 + (x - b + c)^2 = 0\), we can follow these steps: ### Step 1: Understand the equation The equation states that the sum of two squares is equal to zero. Since squares of real numbers are non-negative, both terms must individually equal zero.
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
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  3. The number of real roots of the equation 2x^(4) + 5x^(2) + 3 = 0, is

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  4. If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0, then a, b, c are...

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  5. If the roots of the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are e...

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  6. If a, b,c are all positive and in HP, then the roots of ax^2 +2bx +c=0...

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  7. If the equation ax^(2)+2bx-3c=0 has no real roots and ((3c)/(4))lta+b,...

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  8. If the roots of the equation x^2+2a x+b=0 are real and distinct and th...

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  9. |[1,cos(alpha-beta), cos alpha] , [cos(alpha-beta),1,cos beta] , [cos ...

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  10. Let alpha "and " beta be the roots of the equation ax^(2)+bx+c=0. Let ...

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  11. ifa=cos(2pi//7)+isin(2pi//7) , then find the quadratic equation whose ...

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  12. The integral value of for which the root of the equation m x^2+(2m-1)x...

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  13. If (1+k) tan^(2) x - 4 tan x-1 + k = 0 has real roots, then which one ...

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  14. If the sum of squares of roots of equation x^(2)-(sin alpha-2)x-(1+sin...

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  15. p, q, r and s are integers. If the A.M. of the roots of x^(2) - px + q...

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  16. If alpha, beta, gamma be the roots of x^(3) + a^(3) = 0 (a in R), then...

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  17. If alpha,beta re the roots of a x^2+c=b x , then the equation (a+c y)^...

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  18. If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, t...

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  19. The common roots of the equation x^(3) + 2x^(2) + 2x + 1 = 0 and 1+ x^...

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  20. If f(x) = sum(k=2)^(n) (x-(1)/(k-1))(x-(1)/(k)), then the product of r...

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