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If ( (x+y)^2=81 ) and (xy=14), what is the value of (x^2+y^2)?यदि ( (x+y)^2=81 ) और (xy=14) है तो (x^2+y^2) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 5353
Using the identity \((x+y)^2=x^2+y^2+2xy\), we get \(x^2+y^2=(x+y)^2-2xy\). Therefore, \(x^2+y^2=81-2(14)=81-28=53\). Hence, 53 is the correct answer. A common error leading to 67 is subtracting only \(xy\) instead of \(2xy\). Exam tip: always account for the \(2xy\) term when finding the sum of squares.सर्वसमिका \,\((x+y)^2=x^2+y^2+2xy\) से \,\(x^2+y^2=(x+y)^2-2xy\) होगा। अतः \,\(x^2+y^2=81-2(14)=81-28=53\)। इसलिए सही उत्तर 53 है। 67 प्राप्त करने में प्रायः \,\(2xy\) के स्थान पर केवल \,\(xy\) घटाने की गलती होती है। परीक्षा टिप: वर्ग योग निकालते समय \,\(2xy\) पद को अवश्य शामिल करें।
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