The function $$\(\mathrm{f}\)$$ is defined by $$\(\mathrm{f}(x)=2 x^{2}+3\)$$ for $$\(x \geqslant 0\)$$. Solve the equation $$\(\operatorname{ff}(x)=34 x^{2}+19\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s21_qp_12 Year：2021 Question No：5(b)
Answer:
\(
8 x^{4}+24 x^{2}+21=34 x^{2}+19 \Rightarrow 8 x^{4}+24 x^{2}-34 x^{2}+21-19[=0]
\)
\(
8 x^{4}-10 x^{2}+2[=0]
\)
\([2]\left(x^{2}-1\right)\left(4 x^{2}-1\right)\)
\(
\left[x^{2}=1 \text { or } \frac{1}{4} \text { leading to }\right] x=1 \text { or } x=\frac{1}{2}
\)
8 x^{4}+24 x^{2}+21=34 x^{2}+19 \Rightarrow 8 x^{4}+24 x^{2}-34 x^{2}+21-19[=0]
\)
\(
8 x^{4}-10 x^{2}+2[=0]
\)
\([2]\left(x^{2}-1\right)\left(4 x^{2}-1\right)\)
\(
\left[x^{2}=1 \text { or } \frac{1}{4} \text { leading to }\right] x=1 \text { or } x=\frac{1}{2}
\)
Knowledge points:
1.1.5 recognise and solve equations in which are quadratic in some function of
Solution:
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