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diredragon
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[b[1. Homework Statement [/b]
##|4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x| \ge 8*6^x(8^{x-1}+6^x)##
The sets containing the real solutions for some numbers ##a, b, c, d,## such that ##-\infty < a < b < c < d < +\infty## is of the form ##(-\infty, a] \cup [b, c] \cup [d, +\infty)##. Prove it by obtaining the solution set.
So the problem is asking me to solve the inequality by finding some numbers ##a, b, c, d## and find the form of the real solution set that should be in the form given above.
Here is my current work:
1) ##4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x \geq 8*6^x(8^{x-1}+6^x) ##
2) ##4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x \leq -8*6^x(8^{x-1}+6^x) ##
1)
##2^{6x}-2^{4x+2}*3^{x+1}+20*2^{2x}*3^{2x} \geq 8*3^x*2^x(2^{3x-3}+2^x*3^x) ##
##2^{6x}-12*2^{4x}*3^{x}+20*2^{2x}*3^{2x} \geq 8*3^{2x}*2^{2x}+8*3^{x}*2^{4x-3} ##
##2^{6x}-12*2^{4x}*3^{x}+12*2^{2x}*3^{2x} \geq 3^{x}*2^{4x} ##
##2^{6x}-13*2^{4x}*3^{x}+12*2^{2x}*3^{2x} \geq 0 ##
##2^{4x}-13*2^{2x}*3^{x}+12*3^{2x} \geq 0 ##
2)
##2^{4x}-11*2^{2x}*3^{x}+28*3^{2x} \leq 0 ##
not sure now how to continue, am i on the right track? (latex: messed up something again, can't find what.)
##|4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x| \ge 8*6^x(8^{x-1}+6^x)##
The sets containing the real solutions for some numbers ##a, b, c, d,## such that ##-\infty < a < b < c < d < +\infty## is of the form ##(-\infty, a] \cup [b, c] \cup [d, +\infty)##. Prove it by obtaining the solution set.
Homework Equations
The Attempt at a Solution
So the problem is asking me to solve the inequality by finding some numbers ##a, b, c, d## and find the form of the real solution set that should be in the form given above.
Here is my current work:
1) ##4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x \geq 8*6^x(8^{x-1}+6^x) ##
2) ##4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x \leq -8*6^x(8^{x-1}+6^x) ##
1)
##2^{6x}-2^{4x+2}*3^{x+1}+20*2^{2x}*3^{2x} \geq 8*3^x*2^x(2^{3x-3}+2^x*3^x) ##
##2^{6x}-12*2^{4x}*3^{x}+20*2^{2x}*3^{2x} \geq 8*3^{2x}*2^{2x}+8*3^{x}*2^{4x-3} ##
##2^{6x}-12*2^{4x}*3^{x}+12*2^{2x}*3^{2x} \geq 3^{x}*2^{4x} ##
##2^{6x}-13*2^{4x}*3^{x}+12*2^{2x}*3^{2x} \geq 0 ##
##2^{4x}-13*2^{2x}*3^{x}+12*3^{2x} \geq 0 ##
2)
##2^{4x}-11*2^{2x}*3^{x}+28*3^{2x} \leq 0 ##
not sure now how to continue, am i on the right track? (latex: messed up something again, can't find what.)
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