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3 years ago

If y = -x² + 14x + 7 , then x = 10 is a counterexample for which conjecture?

Mathematics

1 answer:

Misha Larkins [42]3 years ago

6 0

Answer:

The correct answer is B

Step-by-step explanation:

If we plug in x=10 to the equation, we get y=47

Since y is positive, A is not an counterexample

Since y is a function of x, C is not an counterexample

Since the graph of y is a parabola, D is not an counterexample

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2^x - 3^x = √(6^x - 9^x)

dmitriy555 [2]

Answer to the miscellaneous equation, is x=0

Miscellaneous equation are the equations which are not polynomial.

The question can be solved by:

Factorising:Splitting the terms to find the required solution

Completing the squares, etc

2ˣ -3ˣ=√(6ˣ-9ˣ)

-> (2ˣ -3ˣ)²=(3ˣ.2ˣ - 3²ˣ)

Squaring both sides,

-> 2²ˣ+3²ˣ- 2.3ˣ.2ˣ=(3ˣ.2ˣ - 3²ˣ)

-> 2²ˣ+2.3²ˣ-2.3ˣ.2ˣ-3ˣ.2ˣ=0

Factorising the terms,

-> 2ˣ(2ˣ-3ˣ) -2.3ˣ(2ˣ-3ˣ)=0

-> (2ˣ-3ˣ)(2ˣ-2.3ˣ)=0

Equating the braces to zero,

x=0 is the only solution.

Therefore, x =0 is the only solution

Learn more about miscellaneous equation: brainly.com/question/1214333

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