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Problem: In case of what \( a \) the equation \( -10 a-10|a-x|-85=-15 x-x^{2} \) has at least one root in an interval \( (3 ; 7) \) ?

17.34 USE problems

0 $

Problem: In case of what values of the parameter \( a \) the equation \( -4 a+4|a-x|+51=11 x-x^{2} \) has at least one solution in an interval \( (6 ; 9) \) ?

17.35 USE problems

0 $

Problem: What is the parameter \( a \), if the equation \( \left|x^{2}-25\right|=6|x-a|-12 a \) has exactly two solutions?

17.36 USE problems

3.75 $

Problem: In case of what values of the parameter \( p \) the equation \( |x-16|=6|x-p|+2 p \) has exactly three solutions?

17.37 USE problems

2.5 $

Problem: Find the values of the parameter \( a \), for which the equation has exactly 3 solutions. \[ \left|x^{2}-25\right|=8|x-a|-6 a \text {. } \]

17.38 USE problems

3.75 $

Problem: Find the values of the parameter \( a \), for which the equation has exactly 3 roots: \[ \left|x^{2}-16\right|=6|x-a|+2 a \text {. } \]

17.39 USE problems

3 $

Problem: Find all values of the parameter \( a \), for which the equation \( \left|x^{2}-36\right|=8|x-a|-10 a \) has exactly one solution.

17.40 USE problems

2.5 $

Problem: Find all values of the parameter \( a \), for which the smallest value of the function \( y=4 a x+\left|x^{2}-8 x+7\right| \) is greater than 1 .

17.41 USE problems

2 $

Problem: Find all values of the parameter \( a \), for which the minimum value of the function \( f(x)=4 x^{2}-4 a x+a^{2}-2 a++2 \) on the segment \( x \in[0 ; 2] \) is equal to 3 .

17.20 USE problems

0 $

Problem: Find all the values of the parameter for which the roots of the equation \( (1+k) x^{2}-3 k x+4 k=0 \) belong to the segment \( [0 ; 5] \) ?

17.3 USE problems

3.25 $

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