sepia
Lv 7
sepia asked in Science & MathematicsMathematics · 2 years ago

# How will you prove that (√(4 - √7) = (√(8 + 3√7) - 2√2))?

Relevance
• 2 years ago

L.H.S.

= (√(4 - √7))

= (√7 - 1)/√2

R.H.S.

= (√(8 + 3√7) - 2√2))

= (√7 - 1)/√2

Hence LHS = RHS

• 2 years ago

4 - √7 = (1/2)(8 - 2√7) = (1/2)(7 - 2√7 + 1) = (1/2)(√7 - 1)^2

√(4 - √7) = (1/√2)(√7 - 1)

8 + 3√7 = (1/2)(16 + 2*3√7)/2 = (1/2)(7 + 2*3√7 + 9) = (1/2)(√7 + 3)^2

√(8 + 3√7) - 2√2 = (1/√2)(√7 + 3) - (4/√2) = (1/√2)(√7- 1)

Therefore

√(4 - √7) = √(8 + 3√7) - 2√2

• JOHN
Lv 7
2 years ago

• atsuo
Lv 6
2 years ago

Given equation : √(4 - √7) = √(8 + 3√7) - 2√2

Both sides of given equation are positive ,

so if [√(4 - √7)]^2 = [√(8 + 3√7) - 2√2]^2 then the given equation is proved .

[√(4 - √7)]^2 = 4 - √7

And

[√(8 + 3√7) - 2√2]^2

= 8 + 3√7 - 4√((8 + 3√7)*2) + 8

= 16 + 3√7 - 4√(16 + 6√7)

= 16 + 3√7 - 4√[(3 + √7)^2]

= 16 + 3√7 - 4(3 + √7)

= 4 - √7

So , [√(4 - √7)]^2 = [√(8 + 3√7) - 2√2]^2 .

Therefore , √(4 - √7) = √(8 + 3√7) - 2√2 .

Lv 7
2 years ago

Parentheses are unbalanced

• 2 years ago

Work from one side to get to the other! In this case start from the right side and power both parts by two and do the math and I think you’ll end up with the other side! Just make sure to take the square root of the resault since you powered it by 2 in the beginning

• alex
Lv 7
2 years ago

What is (√(4 - √7) ?

Is that (√(4 - √7))

or

√(4 - √7) ?