(15)平方根の式の値(解答) | 学習日 月 日( ) | |||||
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x=√5, y=√3+1のとき, 次の式の値を求めなさい。 |
a+b=3√2, ab=3のとき, 次の式の値を求めなさい。 |
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1 | (x+6)(x−8)−x(x−3) = x2−2x−48−x2+3x = x−48 = √5−48 |
1 | a2b+ab2 = ab(a+b) = 3×3√2 = 9√2 |
2 | (x+1)2−2x = x2+2x+1−2x = x2+1 = (√5)2+1 = 6 |
2 | (a+1)(b+1) = ab+a+b+1 = 3+3√2+1 = 4+3√2 |
3 | y2−2y+1 = (y−1)2 = (√3+1−1)2 = 3 |
3 | a2+b2 = (a+b)2−2ab = (3√2)2−2×3 = 18−6 = 12 |
4 | 7(y−3)−2(3y−5) = 7y−21−6y+10 = y−11 = √3+1−11 = √3−10 |
4 | (a−b)2 = (a+b)2−4ab = (3√2)2−4×3 = 18−12 = 6 |
5 | x(x−y)+y(x+y) = x2−xy+xy+y2 =x2+y2 = (√5)2+(√3+1)2 = 5+(3+2√3+1) = 9+2√3 |
5 | a2b2+2ab = ab(ab+2) = 3×(3+2) = 15 |
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