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Question 1114992: 𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝟑.
(a) Solve the the equation 3x2 − 14x > −16
(b) Using the 𝐈𝐧𝐯𝐞𝐫𝐬𝐞 𝐌𝐞𝐭𝐡𝐨𝐝,solve the system below:
x + 4y = 2 − z
3x + 2y − 2z = −9
y + 3z = 4x + 7
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (a) Solve the the equation 3x2 − 14x > −16
3x^2-14x+16 > 0
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Solve 3x^2-14x+16 = 0 to find the roots.
x = 2 or x = 2.667
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Draw a number line ; plot x = 2 and x = 2.667
Check each of the three resulting intervals on the number
line to find solutions for the inequality::
Check x= 0 in the left interval::3*0-14*0+16 > 0 ;true ; solutions in (-oo,2]
Check x =2.5 in middle interval:: 3(6.25)-14(2.5)+16>0; false no ans in (2,2.667]
Check x =10 in right interval:3(100)-14(10)+16>0; true;solutions in (2.66666,+oo)
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(b) Using the 𝐈𝐧𝐯𝐞𝐫𝐬𝐞 𝐌𝐞𝐭𝐡𝐨𝐝,solve the system below:
x + 4y = 2 − z
3x + 2y − 2z = −9
y + 3z = 4x + 7
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Rearrange::
x + 4y + z = 2
3x+2y-2z = -9
4x-y-3z = -7
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Invert the coefficient 3x3 matrix to get
0.17..0.14..-0.04
0.23..-0.44..0.04
0.03..-0.04..0,04
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Multiply that times the column vector [2..-9..-7] to get
x =-0.66
y = 4.16
z = 0.16
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Cheers,
Stan H.
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