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If (f(x)=x^2+6x+10) and (g(x)=x^2+6x+14), what is the minimum value of (\frac{f}{g})?यदि (f(x)=x^2+6x+10) और (g(x)=x^2+6x+14) हैं, तो (\frac{f}{g}) का न्यूनतम मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{1}{5})(\frac{1}{5})
(\frac{f}{g}=\frac{(x+3)^2+1}{(x+3)^2+5}), which gives the minimum (\frac{1}{5}) at ((x+3)^2=0). It is useful to set the common square term as (t\ge 0).(\frac{f}{g}=\frac{(x+3)^2+1}{(x+3)^2+5}), जो ((x+3)^2=0) पर न्यूनतम (\frac{1}{5}) देता है। समान वर्ग पद को (t\ge 0) मानना उपयोगी है।
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