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Substitution, equivalent expressions and quadratic identities.
Free examples and worked answers. No account needed.
Practise the method.
Substitution, equivalent expressions and quadratic identities.
Substitution, equivalent expressions and quadratic identities.
Example 1
u+v=15 and uv=56. Find (u−v)2.
Show worked answer
Answer: 1
- (u−v)2=(u+v)2−4uv=152−4×56=1.
Example 2
For every x,(x+2)(x+k)−(x+6)2=−3x+q. Find q.
Show worked answer
Answer: −22
- The x coefficient gives 2+k−12=−3
- k=7.
- The constant is q=2×7−62=−22.
Example 3
For every x,(x+p)(x+q)−(x+3)(x+6)=9x+59. Find p2+q2.
Show worked answer
Answer: 170
- Compare coefficients: p+q=18 and pq=77.
- Then p2+q2=(p+q)2−2pq=170.
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