Find a counterexample to show that the following conjecture is false. Conjecture: For all numbers x,(x+4)2=x2+16.

Q: -1- xy(3 + x)-x²y + 10r

A: Given -1-xy(3+x)-x2y+10x

Q: If m∠2 = 6x + 8 and m∠6 = 8x – 6, find the value of x so that ℓ ║ m.

A: GIVEN, If m∠2 = 6x + 8 and m∠6 = 8x – 6, THEN m∠2 = m∠6 { If lines are parallel slope is same)

Q: Find the quotient of (x/2 - 2/x) and (1 - x2/4). What are the restrictions on the variable?

A: We have to find the quotient of the given two expression.

Q: Let P(x) = ax² + bx³ + x +1 where a and b are real numbers. Find values of a and b such that P(2i) =…

A:

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: (d) 2√2-7 = 16 x 22 X

A: given  2x-7=16 if ax=ay,  than x=y

Q: Find the product. Assume variables represent positive real numbers. 2) 2x2/5(x11/5-3x) A)2x13/5 -…

A:

Q: Show that (x? + y²)² = (x² – y²)² + (2xy)? for all real numbers x and y.

A: We have to prove algebraically that x2+y22=x2-y22+2xy2 Simplifying both the sides , we get Here ,…

Q: how that Q(√2 + √3) =Q(√2,√3).

A:

Q: If f(x) = x³ + x4 + ax³ + 4x² – : 32x + b is divisible by x² – 36, find the values of a and b.

A: We will find out the required values.

Q: 4. Use the Binomial Theorem to expand and simplify: (2x– 3y)*

A:

Q: hat are all the real zeros of y=(x-12)3-7?

A: We have to find the real zeros of y=(x-12)3-7.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.