Example Question - variable manipulation
Here are examples of questions we've helped users solve.
Algebraic Expression Transformation
<p>令 \( y + \frac{1}{y} = b \)</p> <p>要表达 \( y^{2} + \frac{1}{y^{2}} \)，首先将原方程两边平方:</p> <p>\( (y + \frac{1}{y})^{2} = b^{2} \)</p> <p>展开左边，应用平方差公式得到:</p> <p>\( y^{2} + 2 \cdot y \cdot \frac{1}{y} + \frac{1}{y^{2}} = b^{2} \)</p> <p>简化得到:</p> <p>\( y^{2} + 2 + \frac{1}{y^{2}} = b^{2} \)</p> <p>现在将方程两边同时减去2:</p> <p>\( y^{2} + \frac{1}{y^{2}} = b^{2} - 2 \)</p> <p>因此，\( y^{2} + \frac{1}{y^{2}} \) 表达为 \( b \) 的项是:</p> <p>\( y^{2} + \frac{1}{y^{2}} = b^{2} - 2 \)</p>
Solving an Equation with One Variable
لحل المعادلة الموجودة في الصورة، نحتاج إلى إيجاد قيمة المتغير \( u \) الذي يجعل المعادلة صحيحة. المعادلة المعطاة: \[ \frac{14}{u} = \frac{2}{3} \] لحل هذه المعادلة وإيجاد قيمة \( u \)، نتبع الخطوات التالية: 1. نضرب كلا الطرفين في \( u \) للتخلص من المقام. \[ u \times \frac{14}{u} = \frac{2}{3} \times u \] \[ 14 = \frac{2}{3} \times u \] 2. الآن نضرب كلا الطرفين في 3 للتخلص من الكسر. \[ 3 \times 14 = 2 \times u \] \[ 42 = 2u \] 3. نقسم الطرفين على 2 لإيجاد قيمة \( u \). \[ \frac{42}{2} = \frac{2u}{2} \] \[ 21 = u \] إذًا، قيمة \( u \) هي 21.
Solving Linear Equation for x
The equation in the image is: \[x + 3 = 5x - 1\] To solve the equation for \(x\), follow these steps: 1. Get all terms containing \(x\) on one side of the equation and the constant terms on the other side. You can do this by subtracting \(x\) from both sides to get all the \(x\)'s on one side, and adding \(1\) to both sides to get all the constants on the other side. \[x - x + 3 + 1 = 5x - x - 1 + 1\] Simplifying this gives: \[4 = 4x\] 2. Now, to solve for \(x\), divide both sides of the equation by \(4\): \[\frac{4}{4} = \frac{4x}{4}\] This simplifies to: \[1 = x\] So, the solution to the equation is: \[x = 1\]
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