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For a in R, if |x - a + 3| + |x-3a|=|2x...

For a `in` R, if `|x - a + 3| + |x-3a|=|2x - 4a +3 |` is ture `AA x in`R. Then find the value of a.

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To solve the equation \( |x - a + 3| + |x - 3a| = |2x - 4a + 3| \) for all \( x \in \mathbb{R} \), we need to analyze the conditions under which the equation holds true. ### Step 1: Analyze the modulus expressions The equation consists of three modulus terms. We can rewrite the equation as: \[ |x - (a - 3)| + |x - 3a| = |2x - (4a - 3)| \] ...
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CENGAGE ENGLISH-THEORY OF EQUATIONS-ILLUSTRATION
  1. Find the least value of n such that (n-2)x^2+x+n+4>0,AAx in R ,w h e ...

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  2. Given that a ,b ,c are distinct real numbers such that expressions a x...

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  3. For a in R, if |x - a + 3| + |x-3a|=|2x - 4a +3 | is ture AA x inR. ...

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  4. If c is positive and 2a x^2+3b x+5c=0 does not have any real roots, th...

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  5. If a x^2+b x+6=0 does not have distinct real roots, then find the leas...

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  6. A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=...

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  7. If the inequality (m x^2+3x+4+2x)//(x^2+2x+2)<5 is satisfied for all x...

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  8. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

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  9. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

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  10. Let x^(2) - ( m - 3) x + m = 0 ( m in R) be a quadratic equation. Find...

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  11. If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbe...

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  12. The equation a x^2-b x+c=0 has real and positive roots. Prove that the...

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  13. For what real values of a do the roots of the equation x^2-2x-(a^2-1)=...

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  14. If (x^2+x=2)62=(a-3)(x^2+x+1)(x^2+x+2)+(a-4)(x^2+x+1)^2=0 has at least...

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  15. Find all real value of a for which the equation x^4 + (a - 1)x^3+ x^2 ...

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  16. If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct ...

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  17. Find all the value of m for which the equation sin^2x+(m-3)sinx+m=0 ha...

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  18. If 2a+3b+6c=0, then prove that at least one root of the equation a x^2...

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  19. Find the value of a for which a x^2+(a-3)x+1 < 0 for at least one posi...

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  20. If x^2+2a x+a<0AAx in [1,2], the find the values of a.

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