Question

Solve it if you can OPEN CHALLENGE TO ALL OF MATHS QUESTIONS
a)4x+6x-8y+3z^2-3x+42358x
b)Find √6(√6√6...)
c)There is a two-digit number whose digits are the same, and has got the following property: When squared, it produces a four-digit number, whose first two digits are the same and equal to the original’s minus one, and whose last two digits are the same and equal to the half of the original’s. Find that number.
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Answer 1

Answer:

Equation of the given tangents are-

t1:3x−4y+4=0

t2:6x

Letx=6+6+6+6+...∞

On squaring both sides,

x2=6+6+6+6+6+...∞

x2=6+x                            

x2−x−6=0

x=2(1)1±12−4×1×(−6)

x=21±25=21±5

∴x=3 or x=−2

Since a negative number cannot be under root, hence x=3

−8y−7=0⇒3x−4y−27=0

Here,

a=3,b=−4,c1=4,c2=−27

Since slopes of the given tangents are equal, i.e., 43

∴ the given tangents are parallel.

As we know that, the distance between two parallel lines given by,

d=a2+b2∣c2−c1∣

∴ distance between t1&t2=32+(−4)2∣∣∣∣∣∣4−(−27)∣∣∣∣∣∣=

Answer 2

Step-by-step explanation:

a) 4x+6x-8y+3z^2-3x+42358x

= 4x + 6x -3x + 42358x = 42365x

-8y has no other coefficient with variable y

3z² has no other coefficient with variable z²

Hence, Answer is 42365x - 8y + 3z²

b) √6*(√6√6)14.6969384567

c) The equation should be found or in whole number-coefficients,

which you should find the solutions for x will be either 1.136363, or 8

Original Number: 88.

Check: 88² = 7744