Use binomial expansion to show that 1+5x1−3x≈1+4x+4x2\displaystyle \sqrt{\frac{1+5x}{1-3x}} \approx 1 + 4x + 4x^21−3x1+5x≈1+4x+4x2
A student substitutes x=313\displaystyle x = \frac{3}{13}x=133 into the expansion to find an estimate for 7\sqrt{7}7. Give a reason why the student should not use x=313\displaystyle x = \frac{3}{13}x=133
Substitute x=112\displaystyle x = \frac{1}{12}x=121 into 1+5x1−3x=1+4x+4x2\displaystyle \sqrt{\frac{1+5x}{1-3x}} = 1 + 4x + 4x^21−3x1+5x=1+4x+4x2 to obtain an approximation for 17\sqrt{17}17. Give your answer as a fraction in its simplest form.
408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.