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Text File | 2000-04-02 | 2.7 KB | 259 lines

>12.Equation involving roots. (Auxiliary variable) x-2*P∞^≤±x±-3=0 MYSZEK 2xy EXAMPLE e t101 p10 t0 zr t1 p5 t0 v500 zrm k@ t2 p3 t0 cxm k-m c2m k*m k@ p1 k@m cxm spm k-m c3m k=m c0m ke t3 p6 t0 kem p10 oxm slm2 k? t23 p6 t0 k?m p10 oxm ka t4 p6 t0 kam cqm kn t5 p10 t0 knm k@m cxm kS t6 p5 t0 sdm slm5 kxm cqm shm kxm cqm k^m c2m sdm ke t7 p3 t0 kem p10 oxm kS t8 p5 t0 shm n(m spm k+m c1m n)m ssm spm4 ssm n(m spm3 n)m ke t9 p3 t0 kem p10 oxm kS t10 p5 t0 shm kxm spm k=m k-m kxm spm ;llm com crm kxm2 spm k=m kxm spm ssm sem ssm kxm kS t17 p3 t0 sgm spm ssm slm ssm kcm sdm slm2 kbm kvm shm kxm kvm sgm shm ssm sem ssm kxm sdm ke t9 p3 t0 kem p10 oxm kS t18 p4 t0 shm ssm spm5 ssm kxm sem kb t19 p3 t0 kbm c9m shm spm kb t20 p3 t0 kbm kb kbm ;ke ;t9 ;p2 ;t0 ;kem ;p10 ;oxm kV t21 p2 t0 kVm p10 oxm t22 p3 t0 ze t102 p10 t0 zxm zem e q BLURB 1`We are going to solve the equation: 1`#@x-2*P∞^≤±x±-3=0@. 2`#We open the &Equations& window and write the problem. 2`#To create a root we press &Shift&+&2& keys or the on-screen button. 3`As usual after formulating the problem we press &ENTER&. 23`We ask the program for a hint at the equality sign. 4`#In a new line 4`#(press &Alt&+&Insert& or the on-screen button) 4`#we introduce an auxiliary variable. 5`#To let the program know that this is just an auxiliary 5`#variable we use the substitution symbol "$¨"$ 5`#(press &Ctrl&+&=& or the on-screen button). 5`#When we subsequently use a predefined variable again, 5`#we use the equality sign "$="$. 6`We substitute the new variable into the equation. 7`We press &ENTER& to check our solution. 8`We notice that: 8`#@q^2±-2q-3=(q+1)(q-3)@. 9`We press &ENTER& again. 10`#Our equation has two solutions, 10`#we write them using the connective OR. 17`We go back to the old variables. 18`The first solution is a contradiction and we remove it. 19`We raise both sides to the power "$2"$. 20`#To remove the root sign 20`#we press the &Backspace& button twice. 21`#This is the final result. 21`#We press the &Answer& button. ;21`#We press "&ENTER&" ;21`#&without making any changes& in the expression. 22`Now the problem is solved. 101`#We show how to use 2xy. 101``#"The presentation proceeds automatically." 101``#To move yellow panels use the mouse. 101`#Press ENTER on the KEYBOARD to continue. 102`#In a moment the &Examples& window will appear. 102`You can watch the same presentation again, or 102`#load the next example, or 102`#close the window and solve your own problem.