Jika X1 dan X2 adalah akar akar dari persamaan x²-3x + 7 = 0 maka nilai dari X1² + X2² + 3X1X2 = ... A. 4 B. 10 C. 16 D. 23 E. 30

<p>Ingat... <i>X₁² + X₂² = (X₁ + X₂⁠⁠⁠⁠)² - 2X₁.X₂</i></p><p><i>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; X₁.X₂ = c/a</i></p><p><i>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;X₁+ X₂ = -b/a</i></p><p>&nbsp;</p><p>Pada soal diketahui: a=1 , b = -3 , c=7</p><p>Sehingga,&nbsp;</p><p>X₁²+X₂² + 3X₁.X₂= (X₁+X₂)²–2X₁.X₂ + 3(c/a)&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= (-b/a)² - 2(c/a) + 3(c/a)&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= (-b/a)² + c/a</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= [-(-3)/1]² + 7/1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 9 + 7</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 16 <strong>(Jawab : C)&nbsp;</strong></p>