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If \((x-k)^2=x^2-30x+225\), find the value of \(k\).यदि \((x-k)^2=x^2-30x+225\), तो \(k\) का मान ज्ञात कीजिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(15\)\(15\)
Expand the left side:
\[
(x-k)^2=x^2-2kx+k^2.
\]
Compare with \(x^2-30x+225\). The coefficient of \(x\) gives
\[
-2k=-30\Rightarrow 2k=30\Rightarrow k=15.
\]
Check constant term: \(k^2=15^2=225\), which matches.
So \(k=15\).बाएँ पक्ष का विस्तार कीजिए:
\[
(x-k)^2=x^2-2kx+k^2.
\]
इसे \(x^2-30x+225\) से मिलाइए। \(x\) का गुणांक देता है:
\[
-2k=-30\Rightarrow 2k=30\Rightarrow k=15.
\]
अब स्थिर पद जाँचिए: \(k^2=15^2=225\), जो मेल खाता है।
अतः \(k=15\) है।
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