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The product of two consecutive positive even integers is 528. What is the smaller number?दो लगातार धनात्मक सम संख्याओं का गुणनफल 528 है। छोटी संख्या क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 2222
Let the smaller number be x. The next consecutive even number is x+2, so x(x+2)=528. This gives x²+2x−528=0, which factors as (x−22)(x+24)=0. Since the numbers are positive, x=22; hence the numbers are 22 and 24. Exam tip: consecutive even integers always differ by 2.छोटी संख्या को x मानें। अगली लगातार सम संख्या x+2 होगी, इसलिए x(x+2)=528। इससे x²+2x−528=0, अर्थात् (x−22)(x+24)=0। धनात्मक संख्या होने के कारण x=22 लिया जाएगा; अतः संख्याएँ 22 और 24 हैं। परीक्षा-युक्ति: लगातार सम संख्याओं का अंतर हमेशा 2 होता है।
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