Qno 11 plz provide a detailed solution Share with your friends Share 0 Aarushi Mishra answered this 3x+4x=5Note: If x<0, then both of 3x and 4x will be negative but R.H.S.is positive,therefore, x cannot be negative. Hence x>0 and thus both of 3x and 4x are non-negativeNow let us look at the solution of following equationa+b=5, where a and b are non-negative integers integers1+4=52+3=54+1=50+5=55+0=5Possible non-ordered pairs of a,b are 1,4, 2,3 and 0,5Note:3<43x<4x⇒3x≤4xCase 1: Let 3x=1 and 4x=43x=11≤3x<21≥x3>123≥x>32 ___________14x=44≤4x<514≥x4>151≥x≥45 _________2From 1 and 2 we can see there is no solutionCase 2: Let 3x=2 and 4x=33x=22≤3x<312≥x3>1332≥x>1 ___________14x=33≤4x<413≥x4>1443≥x≥1 _________2From 1 and 2 we can see there a common interval which is the solutionThus x∈(1,43] Case 3: Let 3x=0 and 4x=53x=00≤3x<1∞≥x3>1∞≥x>3x>3 ___________14x=55≤4x<615≥x4>1645≥x≥23 _________2From 1 and 2 we don't have any solutionNowSolution is x∈(1,43]Comparing with x∈(a,bc]a=1, b=4 and c=3a+b+c+abc=1+4+3+12=20 0 View Full Answer
