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Prove that the square of an odd number is always 1 more than a multiple of 4

(2x-1)² = 4x²- 4x + 1= 4(x²-x)+1The part of the expression which is: 4(x²-x) indicates that the value is a multiple of 4. The number 1 is then added which means...

Answered by Gokul P. • Maths tutor

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4y^2 = 256, Find a value for y

y^2 = 256/4 = 64
therefore, y = sqrt(64) = 8

Answered by Kai P. • Maths tutor

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A circle with centre C has equation x^2+8x+y^2-12y=12. The points P and Q lie on the circle. The origin is the midpoint of the chord PQ. Show that PQ has length nsqrt(3) , where n is an integer.

First complete the square for both x and y. Move all constants to the right hand side. The square root of this is the radius of the circle. The two constants in the completed square bracket show the x and...

Answered by • Maths tutor

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Solve the simultaneous equations: 2x + y = 12; x - y = 6

We add the two equations together (left-hand sides and right-hand sides separately). By doing this we get: 2x + y + (x - y) = 12 + 6. By rearranging and simplifying: 3x = 18.If we divide both sides by 3 w...

Answered by Rebeka D. • Maths tutor

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Integrate(1+x)/((1-x^2)(2x+1)) with respect to x.

To simplify the fraction first notice (1-x²) = (1-x)(1+x) so the common factor of (1+x) in the numerator and denominator can be cancelled. (1+x)/((1-x^2)(2x+1)) = 1/((1-x)(2x+1)), then we need ...

Answered by Ravinder H. • Maths tutor

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