IIT JEE , AIEEE Forum - Mathematics , Trignometry

ssbrightstar1

Find the minimum value of $\sqrt{X sqr - Y sqr}$ sorry not minus but root under X square + Y square if 5X+12Y=60

risin

The answer is 720/13?

ssbrightstar1

please derive, explain

risin

Let's say the value is z $Z=\sqrt[]{X^2 + Y^2} \\It\;is\;like\;a\;circle\;with\;radius\;z\;and \;the\;given \;equation\;is\;the\;tangent\\So,it\;satisfies\;the\;equation\;y=mx+c\;where\;c=\pm z\sqrt[]{1+m^2}\\Therefore,\\60=z\sqrt[]{1+\frac{25}{144}}\\or\\60=z\frac{13}{12}\\=>z=\frac{720}{13}\$ .

celestine

60/13

hsbhatt

By Cauchy-Schwarz Inequality

$(x^2+y^2)(5^2+12^2) \ge (5x+12y)^2$

Hence $\sqrt{x^2+y^2} \ge \frac{60}{13}$

ssbrightstar1

Thanx sir.

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