Factorise : х^2 - 9y^2 + 6у – 1
Step By Step Explanation
Answers
Answer:
x²-9y²+6y-1
Step-by-step explanation:
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\underline{SOLUTION}
SOLUTION
➡
\begin{gathered}\underline{Given :}\: \\ \\ 2x + 6y = 60 \\ \\ xy = 1 \\ \\ \\ \underline{To \: \: find \: :} \: \: x {}^{2} + 9y {}^{2}\end{gathered}
Given:
2x+6y=60
xy=1
Tofind:
x
2
+9y
2
\begin{gathered}Now, \\ \\ 2x + 6y = 60 \\ \\ = > 2(x + 3y) = 60 \\ \\ = > x + 3y = \frac{60}{2} \\ \\ = > x + 3y = 30 \: - - - - > (1)\end{gathered}
Now,
2x+6y=60
=>2(x+3y)=60
=>x+3y=
2
60
=>x+3y=30−−−−>(1)
Squaring \: \: both \: \: sides \: \: of \: (1) \: \: we \: \: get,Squaringbothsidesof(1)weget,
\begin{gathered}(x + 3y) {}^{2} = (30) {}^{2} \\ \\ = > x {}^{2} + 2 \times x \times 3y + 9y {}^{2} = 900 \\ \\ = > x {}^{2} + 9y {}^{2} + 6xy = 900 \\ \\ = > x {}^{2} + 9y {}^{2} + 6 \times 1 = 900 \: \: \: \: (as \: \: xy \: = 1 \: \: given)\\ \\ = > x {}^{2} + 9y {}^{2} + 6 = 900 \\ \\ = > x {}^{2} + 9y {}^{2} = 900 - 6 \\ \\ = > x {}^{2} + 9y {}^{2} = 894\end{gathered}
(x+3y)
2
=(30)
2
=>x
2
+2×x×3y+9y
2
=900
=>x
2
+9y
2
+6xy=900
=>x
2
+9y
2
+6×1=900(asxy=1given)
=>x
2
+9y
2
+6=900
=>x
2
+9y
2
=900−6
=>x
2
+9y
2
=894
\underline{ANSWER}
ANSWER
➡
\boxed{x {}^{2} + 9y {}^{2} = 894}
x
2
+9y
2
=894
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Answer:
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