1. Simplify the expression $ rac{1}{ rac{1}{ rac{1}{2}- rac{1}{5}}}$.
2. Expand and rearrange to get $x^2 - 4x - 1 = 0$.
3. For values of $x$ in the form $a + b\sq... show full transcript
Worked Solution & Example Answer:1. Simplify the expression $ rac{1}{ rac{1}{ rac{1}{2}- rac{1}{5}}}$ - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 1
Step 1
Simplify the expression $ rac{1}{ rac{1}{ rac{1}{2}- rac{1}{5}}}$
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Answer
To simplify the expression, start by calculating the denominator:
Find the least common denominator of 2 and 5, which is 10:
rac{1}{2} - rac{1}{5} = \frac{5}{10} - \frac{2}{10} = \frac{3}{10}
Substitute back into the original expression:
1031=310
Step 2
Expand and rearrange to get $x^2 - 4x - 1 = 0$
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Answer
Let’s assume we have a quadratic equation in standard form:
Begin with the equation:
ax2+bx+c=0
For the given quadratic equation, rearrange it to the form:
x2−4x−1=0
Rearranging requires moving all terms to one side of the equation.
Step 3
For values of $x$ in the form $a + b\sqrt{c}$ where $a$ and $b$ are fractions
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Answer
To find the solutions for the quadratic equation:
Use the quadratic formula:
x=2a−b±b2−4ac
Substituting a=1, b=−4, and c=−1 gives:
x=2(1)4±(−4)2−4(1)(−1)=24±16+4=24±20
Simplifying further:
x=24±25=2±5
Therefore, the solutions are:
x=2+5andx=2−5
