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The-minimum-value-of-the-expression-B-z-2-z-3-2-z-6i-2-is-p-What-the-value-of-p-10-

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Question Number 131196 by john_santu last updated on 02/Feb/21
The minimum value of the expression B = ∣z∣^2 +∣z−3∣^2 +∣z−6i∣^2 is p. What the value of (p/(10)) .?
TheminimumvalueoftheexpressionB=∣z∣2+∣z−3∣2+∣z−6i∣2isp.Whatthevalueofp10.?
Answered by liberty last updated on 02/Feb/21
z=a+bi → { ((∣z∣^2 =a^2 +b^2 )),((∣z−3∣^2 = (a−3)^2 +b^2 )),((∣z−6i∣^2 = a^2 +b^2 +36−12b)) :} now we find B=3a^2 +3b^2 −6a−12b+45 B=3(a−1)^2 +3(b−2)^2 +30 so the minimum value of B is 30 when { ((a=1)),((b=2)) :} ⇒ z=1+2i then p = 30 and (p/(10)) = ((30)/(10)) = 3.
z=a+bi→{∣z∣2=a2+b2∣z−3∣2=(a−3)2+b2∣z−6i∣2=a2+b2+36−12bnowwefindB=3a2+3b2−6a−12b+45B=3(a−1)2+3(b−2)2+30sotheminimumvalueofBis30when{a=1b=2⇒z=1+2ithenp=30andp10=3010=3.
Commented by john_santu last updated on 02/Feb/21
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