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If (x+y=13) and (xy=40), what is the value of (x^2+y^2)?यदि (x+y=13) और (xy=40) हो तो (x^2+y^2) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 8989
Using the identity \((x+y)^2=x^2+y^2+2xy\), we get \(x^2+y^2=(x+y)^2-2xy\). Therefore, \(x^2+y^2=13^2-2(40)=169-80=89\). Option 169 is only \((x+y)^2\); subtracting \(2xy\) is necessary. Exam tip: when the sum and product are given, start with \((x+y)^2-2xy\).सर्वसमिका \,\((x+y)^2=x^2+y^2+2xy\) से \,\(x^2+y^2=(x+y)^2-2xy\) होगा। अतः \,\(x^2+y^2=13^2-2(40)=169-80=89\)। विकल्प 169 केवल \,\((x+y)^2\) है, जबकि इसमें से \,\(2xy\) घटाना आवश्यक है। परीक्षा टिप: योग और गुणनफल दिए हों तो पहले \,\((x+y)^2-2xy\) वाली सर्वसमिका लिखें।
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